Free-kicks from Alexander Kolarov and James Milner either side of a Sergio Aguero goal, sent the champions on their way to a comfortable home win, with Joe Hart rarely tested throughout the afternoon.
The match also represented City's first consecutive wins in the league this term and the Italian was satisfied with his charges' improvement against the Black Cats, after only winning one point against the Wearsiders last term.
"It's the first time! We are very happy, for the victory but also for the clean sheet," Mancini told Sky Sports.
"There are sometimes when we were unlucky, we didn't deserve to concede against Fulham, against Stoke, two strange goals.
|ANOTHER CLEAN SHEET?
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"Today, I think we had a very good performance. 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 is 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."
The 47-year-old praised the impact of substitute Sergio Aguero, who entered the match as a second-half substitute and netted City's second goal just four minutes later.
"He's fantastic," he said. "His impact was fantastic, he scored one goal and had other chances."
Black Cats boss Martin O'Neill was frustrated with his side's sloppiness in possession, but conceded that the hosts were too good for his men to deal with.
"They are a very fine side," the Ulsterman said. "Initially we didn't help matters, couldn't keep the ball too well, but we were beaten by a much better side.
"I thought we should have done better in the first-half period. We had opportunities, but we gave the ball away too easily, having said that at half-time we were still in the game but we were well beaten in the second half.
"While the game was still 1-0 we were still in with a chance but the more you press forward the more gaps you leave and they are more equipped than anyone to deal with that."