Mancini pleased with Man City victory in Community Shield
He said: "It was a good performance. When Chelsea were leading 1-0, we played better.
"With the sending-off, it was difficult to see from the bench but it is an advantage to play with an extra player.
"It had an impact on the game. It is impossible to say no because 11 versus 11 is different. But we played better than Chelsea, played better football."
Chelsea boss Roberto Di Matteo claimed the red card issued by referee Kevin Friend was the key moment in the game.
He said: "It changed the game in favour of Manchester City. We competed very well and at that point were in the lead.
"It was difficult in the second half against 10 men.
"The challenge had no intent to hurt the opposition. It was a sliding tackle and he got the ball as well.
"Sometimes a red card is given in those circumstances, sometimes it is not. But there was no intention to harm the opponent."