City ace Dedryck Boyata was sent off after just five minutes for a reckless challenge on Arsenal forward Marouane Chamakh.
“I think it (the sending off) was decisive in the game because it was at the worst moment,” he told Sky Sports.
“But I am very proud of my players because I think they played very well. We stayed in the game until the second goal.
“We tried always to score and play – this is very important.
“I think after today we must say that we are one of the best teams in the Premier League.
“I think that 11 against 11 we would have won this game.
“Okay I am disappointed for the loss but it can happen 11 against 10 against Arsenal.
“After this game I think we have improved a lot, we are a strong team. Now it is past.”
Mancini does not agree that Boyata deserved to be sent off for his tackle on Chamakh.
He added: “I do not agree with the referee.
“I thought the rule is always the last man, if there is a clear opportunity to score a goal, it is a red card.
“But I think when Chamakh touched the ball, the ball was probably going out or on the way to the keeper.”