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 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."
He added: "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."
City were without midfielder Gareth Barry and, as expected, talisman Carlos Tevez did not appear.
Barry was rested as a precaution after a knock while Tevez now has just Tuesday's crunch clash against Champions League-chasing rivals Tottenham to prove his fitness for next week's FA Cup final.
Mancini said of Tevez: "He will need to train with the team and in the next days we will see if it is possible.
"If he can play 20 minutes somehow we can see if he can play or not. At the moment I think 50% for the final."
Source: PA
Source: PA