Quirrell presumivelmente identificou da mesma forma que Harry & Co originalmente identificou:
"They're not birds!" Harry said suddenly. "They're keys! Winged keys — look carefully. So that must mean..." he looked around the chamber while the other two squinted up at the flock of keys. "... yes — look! Broomsticks! We've got to catch the key to the door!"
"But there are hundreds of them!"
Ron examined the lock on the door.
"We're looking for a big, old-fashioned one — probably silver, like the handle."
They each seized a broomstick and kicked off into the air, soaring into the midst of the cloud of keys.
Harry Potter and the Sorcerer's Stone, chapter 16: "Through the Trapdoor" (emphasis mine)
Então, só porque Harry, Ron e Hermione tiveram um atalho (a asa danificada), não significa que Quirrel não poderia ter identificado da maneira mais difícil.
Quanto a como ele conseguiu, eu suponho que ele usou as vassouras, o mesmo que Harry & Co - isso é o que eles estavam lá, afinal.