Palpatine seduced Anakin by promising he could save Padmé using the dark side of the Force. But in the end, he lied that she was killed by Anakin by mistake. Anakin had already turned to the dark side, so she couldn't have been a hurdle. The dark side was powerful enough to save Padmé (think about the virgin birth of Anakin).
So, what was the point behind not keeping his promise?
A few problems, to begin with:
So: Either he couldn't do it, didn't want to do it or both.
HNL has a great answer which has already been accepted, but there is just one more point I'd like to make...
It's not merely that he didn't save Padme, it's that he didn't save Padme from being killed by Anakin. Carelessly killing Padme was a moral point of no return for Vader - after that, he'd be capable of doing anything. If Palpatine were to save Padme in those circumstances, Palpatine would be saving Anakin from himself, which is exactly the opposite of what Palpatine is trying to achieve.
Palpatine didn't really want to save padmé, if she survived she would have been a leader of the Rebellion, and Palpatine didn't like this. So if he also could effectively save her life he didn't want to do it, padmé was his enemy
I don't think the answers get to the point: Padme's death (especially caused by Anakin/Vader himself) makes Vader feel more angry; which is better for the Dark Side.