City defender Deryck Boyata was given his marching orders by referee Mark Clattenburg in just the fifth minute for his challenge on Arsenal striker Marouane Chamakh before the Gunners went on to claim the match 3-0.
But the Italian tactician believes it would have been a much different story if his side had their full quote on the pitch.
"I think against Arsenal it is difficult to play 11 versus 11," he said.
"Ten against 11 is worse, but it is my opinion that we if played 11 against 11 we would have won this game.
"I am very proud of my players because I think they played very well. They tried always to score, always to defend very well.
"I think they showed we are one of the best teams in the Barclays Premier League."
And Mancini added that he thought Clattenburg got it all wrong.
"I do not agree with the referee," he added.
"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."