The former Malaga coach saw his side let two leads slip, conceding three second-half goals in 25 minutes as Leandro Bacuna, Karim El Ahmadi and Andi Weimann secured a memorable victory.
However, while stating his belief in the side's title challenge come the end of the season, Pellegrini insisted City will take each game as they come as they look to bounce back with a win against Everton.
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"I think that we are very strange conceding the first goal which was offside. The second goal wasn’t a free kick and the third goal was drawing 2-2 and at that moment we were going forward.
"I think that we have a lot of chances and a lot of possession. I think we have clear chances to score but we didn’t and we were twice up so I was twice disappointed with that."
Paul Lambert, meanwhile, expressed his delight at his side's resilience to come from behind but rejected notions their third goal proved they were a long-ball team after Brad Guzan's strong influence in the play.
"I thought that was brilliant vision from Brad the way he's done it," he said. "He's got to execute that and he's got a hell of a kick on him. It's not a long ball as in we have kicked it long.
"I don't play the game for Brad. He sees things through his own eyes and I'm not one to tell Brad Guzan how to get the ball out the net and how to distribute it. If I did that I don't think he would thank me for it.
"It's a fabulous achievement against Manchester City because the magnitude of the club and the players that they've got. What's really impressive is that we managed to come back twice against them."