The 2-1 victory means qualification for the Champions League knockouts is in their hands going into the final game with Villarreal.
"We were facing a very strong side in excellent form," said Mazzarri after ending City's run of nine consecutive victories.
"We truly achieved something incredible and I want to enjoy this night. In the first 15 minutes of the second half in particular, we played great football. It wasn't easy to think we could win this, but what we achieved was almost impossible.
"It was already remarkable that we earned a point in Manchester, but in some ways this was even tougher, as we absolutely had to win.
"There was a moment in which we were almost afraid to win. It's an issue of experience. Our ascent has been rapid, but it is not yet complete.
"We could've given more at the end. Sometimes we get taken over by haste, but in the long run we will be able to keep that at bay. I'd like us to learn to win even while playing badly, but only the consolidated clubs can do that and we're not at that level yet."