Samir Nasri opened the scoring on five minutes and City maintained their 1-0 lead until the final quarter of an hour, when the hosts hit a quick-fire treble to turn the game on its head.
"I cannot believe we lost this game" Mancini told BBC Sport. "We had it under control and played very well for 80 minutes.
"This was our problem this year. When we had a chance we did not score, it is the mirror of our season.
"Instead, we did not score, and after, we did two mistakes."
City's defeat means that Manchester United will be crowned champions of England on Monday night if they beat Aston Villa at Old Trafford.