The defender saw red for bringing down Marouane Chamakh when he was the last man, before the Gunners overwhelmed 10-man City with goals from Samir Nasri, Alex Song and Nicklas Bendtner.
The result saw City drop from second to fourth in the table with both Arsenal and Manchester United passing them.
Mancini said: "I think against Arsenal it is difficult to play 11 versus 11. 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."
On Boyata's red card, he said: "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."
Source: PA
Source: PA