City were frustrated in their Champions League push as the Toffees came from behind to deny them a victory that would all but have secured a Barclays Premier League top-four place.
The FA Cup finalists went ahead through Yaya Toure and then squandered a number of chances before Everton hit back through former City defender Sylvain Distin and Leon Osman.
Mancini said: "It was incredible we lost this game. We dominated in the first half and had four or five chances to score. But this is football. If you lose concentration, if you concede a yard to the other team, it is difficult.
"A game like this we should never lose. If we want to become a strong team, we cannot lose this game. We shouldn't lose it because we had more chances to score in the second half.
"It is not important who scores the goals, it is important the team wins the game."
Source: PA
Source: PA