David Silva struck the only goal as City won a pulsating clash at the Etihad Stadium to return to the top of the Barclays Premier League. Mancini felt his players had come through a test of nerve after losing their unbeaten record at Chelsea on Monday and being knocked off the summit by Manchester United earlier on Sunday afternoon.
Mancini said: "I think we deserved to win this game. We had half a chance and Silva scored an important goal. We are on the top again. I am delighted for this because after Chelsea it was really important to beat Arsenal and go again to the top of the table, also because Arsenal are a really strong team at this moment."
The result lifted City two points clear at the top again but Mancini accepts they may not stay there permanently throughout the title race.
The Italian said: "We know United are a really strong team and we can't think that we can win the title without fighting against United. We know it is possible we could go into the second position sometimes because when there are squads like us, United and Tottenham it can happen. But it is important we are there in the end."
When it was pointed out City could now be top at Christmas for the first time since 1929, Mancini said: "We want to stay at the top for a long time, not only Christmas."
City had a number of chances before finally going ahead after 53 minutes, Sergio Aguero firing over and then forcing a save from Wojciech Szczesny, who also denied Mario Balotelli.
Silva slid in his sixth goal of the season after Balotelli had another shot saved and Pablo Zabaleta then hit the post. But Arsenal also tested Joe Hart and had a penalty appeal for handball against Micah Richards turned down.
Arsenal manager Arsene Wenger said: "I haven't seen it, but (Robin) Van Persie is adamant - 100% penalty. It was a game where it could have gone both ways. It was very intense with both teams going for it.
"I felt we were a bit unlucky and their keeper had a good game. We were unlucky as we had to reshuffle at the back in a position where we are already short."
Source: PA
Source: PA