"It's the first time [that we have kept a clean sheet]," Mancini told Sky Sports. "We are very happy for the victory and also for the clean sheet.
"There are sometimes when we were unlucky, we didn't deserve to concede against Fulham, [and] against Stoke, [we conceded] two strange goals.
"But now it's important for [goalkeeper] Joe [Hart]. [On] Wednesday he was fantastic against Borussia [Dortmund in the Champions League]."
Mancini further expressed his delight at City's performance against the Black Cats.
"Today, I think we had a very good performance," said the Italian. "We played very well, didn't take any risks and we scored three goals, but we missed another four or five.
"I'm happy with the performance, it was not easy. Sunderland are a good team and every time they play against us it's a very difficult game.
"I think that all the players that played today played very well, I'm happy for them."
City have moved to second in the league table for the time being with 15 points from seven matches.