The Italian saw his side bounce back from Monday's defeat to Chelsea with a hard earned victory over Arsene Wenger's men but knows his team is in a fight for the title.
A David Silva goal from close range was enough for the Italian's side to move back to the top of the table after a brief stay in second place following Manchester United's win at QPR on Sunday.
Mancini's men will be strong favorites ahead of their clash with Stoke City on Wednesday and despite losing to Chelsea on Monday, a win against the Potters will ensure that City is at the summit of England's top division at Christmas for the first time since 1929.
"We deserved to win this game," Mancini told reporters. "We had a lot of chances and Silva scored an important goal. We are on the top again. We are delighted because after Chelsea it was really important to beat Arsenal and to go on the top of the table and also because Arsenal is a really strong team."
Despite being pleased with the victory, Mancini admitted that his side will have to scrap with its neighbor if it is to win the title come May.
"We know United are a strong team, we can’t think we can win the title without a fight against United, this is impossible," he said. "We know it’s possible that we can go into second position sometimes because when there’s squads like us, United and Tottenham it can happen but it’s important to be top at the end. We want to stay at the top of the table for a very long time, not only Christmas. We want to beat Stoke but they are like Arsenal. They’ve won four games in a row and every game is difficult."
Mancini refused to rule Arsenal out of the title race despite the gap between the two sides growing to 12 points after the game at the Etihad, but the City boss admitted that the Gunners will struggle to challenge.
"It is difficult for them as they are 12 points behind us, 10 points behind United, seven points behind Tottenham but there are a lot of games until the end," he said.