It seems as though the issue here is not that your players were upset by the fact that their characters died, it's that your players were upset by the fact that their characters died Apesar de they wanted to play a "dark, rough, and dangerous" game in which their characters were at risk of dying.

Sometimes, people just get upset.

Psychology is an odd thing. Humans are interestingly able to want something very badly and then be unhappier once they get it. For many people, having your characters die, be wounded, lose equipment, or fail to complete their objectives is upsetting. It's unenjoyable. It makes them angry or frustrated in the same way that losing at a competitive sport can make people angry or frustrated. Defeat is not always an easy thing to take gracefully.

Personally, I recently felt quite disheartened and frustrated when I lost a game of Diplomacy because I'd been betrayed by another player (note: Diplomacy is a board game almost inteiramente concerned with betrayal and backstabbing). Even though I knew from the outset that this was part of the game, and knew that it was ultimately fairly irrational for me to feel upset, the fact remained that I did. It was a natural emotional response to seeing all my plans dashed and my chance of winning slip through my fingers. I found I didn't really care about continuing to play anymore, and even though I tried to convince myself that I should still care, my heart wasn't in it.

Would I play Diplomacy again? Absolutely. But that doesn't change the fact that it hurt to lose, and it hurts to lose in Shadowrun as well. Emotion leaks, and not everyone is good at preventing it from leaking. Even if your players want to be punished harshly for their actions... they still might get upset when they are punished for their actions. This doesn't necessarily mean you shouldn't punish them.

How to minimise people getting upset

So, it might be inevitable that people get upset to some extent. This doesn't mean there aren't things that can be done to avoid it.

If players cause their characters to make legitimately poor decisions that, based on the information they have and their understanding of it, lead to what they consider to be consequently deserved negative outcomes for their characters (and only their characters), then this is the best possible situation with the least amount of upsetness.

But communication is key in every stage of the process.

If players don't have complete information about the expected consequences of their decisions (even if their characters do) then they'll feel cheated when they get negative consequences they feel they couldn't have known about. Particularly in situations where the stakes are high, it can often be a good thing to clearly and explicitly state to the players, out of character, what you think they should know (based on their characters' understanding) what the expected outcomes of their decision are. For example, saying something like "Are you sure you want to jump into the hole? Just so we're clear, it's a fairly long drop and it's too dark for you to tell what's at the bottom, it could be spikes or something, and even if there's nothing bad you might not be able to get back up again." This ensures that the players are making informed decisions (even if it's the informed decision to have their character make an uninformed decision) and clears up any potential misunderstandings before they happen (maybe when the player imagined that hole, he thought it was just a meter or so deep!)

Se o caracteres have incomplete information, it's equally difficult for the players to make realistic decisions. And it's often difficult for characters to get anything more than incomplete information. I recommend erring on the side of being generous when characters act "stupidly" based on what information they've had access to in-world. Yes, there should be some cost to characters choosing to rush in blindly or disregard signs of danger. But clues that are obvious to the GM are often painfully opaque to the players. See some of the answers to a esta pergunta for effective ways to communicate danger to players.

Even if the players and the characters have relatively complete information, there may be a lack of shared understanding as to what exactly constitutes "reasonable consequences". To some groups, character death is something that should be completely off the table. To some groups, significant character-altering bad things (e.g, loss of a limb, new negative Traits) should never happen to a character without the player's express out-of-character permission. Possibly your players think they want a "rough, dark, dangerous" game but their understanding of "dangerous" is different to yours.

This is a good time for you and your players to use the Ferramenta Mesma Página to narrow down what exactly the expectations are.

Okay, I did all that, but they still get still upset! What do I do?

It's not easy to deal rationally with frustrated players. They feel like they've failed and they feel powerless, and consequently they're disincentivised to keep engaging with the game (on both counts: they've been hurt by the fact that they've failed and don't want to be hurt again, and they feel like they have no power to influence events, so why bother?)

If you must make players fail and suffer harsh consequences, you should try to minimise both how hard the failure should hit and how powerless they are as a result. An entirely unrecoverable failure is kind of frustrating even if it's deserved. If they're already frustrated, you should do what you can to give them back some power. If possible, try to do this without entirely eliminating the sharpness of their failure (otherwise it feels like you're just capitulating to their tantrum, which is not what they want and so will not make them feel batter). But show them that even though they've suffered consequences, they haven't lost their ability to achieve their goals. For example, they're badly wounded and they don't think they can successfully contribute to the fight anymore? Reframe the conflict for them personally: give them a chance to get away before the enemy kills them (and oppose them limitedly in that goal rather than in the rest of the party's goal of winning the fight). Or give them a chance to, while wounded, crawl over to the grenade the enemy leader dropped on the ground and toss it. Make them feel like they still have agency.

Finally, if a player is becoming so frustrated and upset that they're making it hard to say that the game is actually fun, it might be time to give them a bit of space. You can:

• switch focus: swap to another section of the party or do a "meanwhile" segment with a group of NPCs or cut backwards or forwards in time
• rush to a conclusion: say that most of the fight goes out of the enemy as soon as the players kill the next one, or say "okay, you kill the rest of them, we don't really need to bother rolling dice, you're going to win eventually", or tell them that enemy reinforcements are arriving in great numbers and they think it's probably a losing battle - do they want to run while they've got the chance?
• if entirely necessary, just stop playing entirely and resume next week when everyone's had a bit of a chance to calm down.

Experiência

The way it looks like now, your players don't seem to know what they really want. Therefore, you should experiment. Prepare a session that's extremely grim and dangerous, and another one where they can come out as heroes. This way, judging from their reactions, you can decide for them what they really want.
If you want, you could inform them of this little experiment you're planning, but it will most likely alter the result.

Motivos

Don't take this for granted, but the way you describe your players I think they don't na realidade want to play in a grim and dangerous world. They want to be the heroes of that world. They don't want to live in that world, they want to fixo it. However, when they realised they aren't able to save the world just yet, they got bummed out.
You could discuss your players' motives with them, and possibly get rid of any misunderstandings in the group.

You may be playing it exactly right. They got upset when something bad happened to them. Different people handle this in different ways. Your guys got bummed out and withdrew a bit. They recovered and got interested in the game again. It at least shows they're quite attached to their characters.

The way to tell if you've done it right is notice if the players are eager for the next session? If they are then you've probably done something right. Especially if they're talking about the fight that happened last time. You may see a more conservative play style from these players.

I really like idea of Joinean's idea of experimenting with play styles. I would add that if your players respond better to the easy sessions then don't always give them easy sessions. Throw in the odd tough one with a load of more obvious foreshadowing to change the pace a bit. You can't enjoy the smooth without some rough.

1

Both players were really pissed that they got wounded and lost interest in the game.

This does not appear to agree with this,

2

I asked them if they wanted a more cinematic battle where they are the heroes, but altogether they said that the current style (it's dark, rough and dangerous) is what they wanted to play.

At risk of sounding like a proponent of Quantum Ogre GMing, it really sounds like they want the excitement of dark, rough and dangerous without the consequences, or rather the ilusão of dark, rough and dangerous. I can't see any other recipe that would meet both requirements (2) rough, dark and dangerous, (1) can't actually get hurt.

Now, to be fair, I would argue, at least long term, running this kind of game's going to lose it's excitement after too many encounters of not being hurt no matter what you do.

Going the other direction, one of the easiest ways to keep players from being angry with you when they get hurt is to be impartial. The players may see you (the GM) as the enemy, instead of the NPC if they believe you escolher the outcome. The more fudging die rolls or changing the environment to favor the PC outcome, the more you will be seen as responsible for the outcomes that aren't favorable.

Boa sorte.

Here is what I do, if the players have gone badly off-script and are about to tackle an encounter that is way too tough for them: I step out of character and I address them directly, and I say: "Hey, here's a warning: you're doing stuff the book assumed you wouldn't do, and this is going to be a really tough battle. Are you sure you want to do this?"

There's a difference, I think, between sending that warning via NPC and sending it as the DM directly. If an NPC sends a warning, the party could dismiss it: that NPC might just be a coward, or might be trying to scare the party away from something, or might be unreliable. Or they might be totally correct that the monsters up ahead are way tougher than normal humans, but they might not have realized that the party can deal with it anyway. When you send the warning yourself, it makes sure the players take it seriously, and tb it communicates that you're on their side and you're hoping they succeed.

Let me say a bit more about the "you're on their side" thing. There's a bad stereotype of the "mustache-twirling" DM, who says things like "Haha, yay! I rolled a critical hit on you!" and "Oh, damn. I was hoping that would kill at least one of you." I believe that it helps the players' mood a lot if you do the exact opposite of that. When I deal someone a lot of damage, I say something like "please tell me you're not dead, I would feel really bad if I killed you."

Overall it sounds like you ran the game pretty well, and it's the players who were unreasonable. But you've asked for advice on how você can do better, so that's what I've offered here.