After playing against 10 men for most of the match, the Premier League champions' win was ruined by a second-half sending off for their captain, which the manager feels was harsh
The City skipper was shown a straight red for an apparent two-footed lunge on Jack Wilshere, after referee Mike Dean had earlier dismissed Arsenal defender Laurent Koscielny for hauling Edin Dzeko to the floor in the penalty area.
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"This is not a red card, absolutely not," he told Sky Sports.
"He has one foot to take the ball, the other is left. I think that the referee made a mistake there.
"It was not a sending off for Vinnie because Vinnie took the ball with only one foot after anticipating the opponent."
Mancini admitted the earlier red card for Koscielny made things easier for his side, but was disappointed they were unable to extend their lead after the break.
"If you play with 10 players it is very difficult," he added.
"But we started the game very well, we played high, pressed high. After the sending off it was easier.
"Second half we were too soft and we missed three or four goals and after the game can be open."
The City boss stressed the importance of picking up a first win at Arsenal in 37 years as they closed the gap on league leaders Manchester United, who had earlier beaten Liverpool to move ten points clear.
"It's important because we know United is strong and probably they could win against Liverpool," he said.
"But the season is long and we need to work."