Robin van Persie scored a stoppage-time winner to give Sir Alex Ferguson's side a 3-2 victory at the Etihad Stadium, ending the defending champions' unbeaten start to the season.
United, who surrendered a 2-0 lead before snatching back all three points at the death, now head into the Christmas period with an imposing advantage but Mancini remains bullish over his side's chances of retaining the title.
"For 20 minutes they didn't touch the ball and the first chance they got, they scored a goal," Mancini said.
"We recovered very well and we dominated the second half. We wanted to win the game and we had chances.
"We have showed we are a really strong team and we can win this title again. We can't win always. There is a moment when you lose at home and it happened today. But the season is a long one.
"We won the league with the last touch of the ball last year. But we didn't deserve to lose this game. We played very well."
Sunday's defeat was City's first home loss in the league since a reversal against Everton in December 2010 and came at the end of a week that saw them crash out of the Champions League with the worst haul of any English club in the competition's history.