Vincent Kompany's header in first-half stoppage-time was all that separated the teams, but they outplayed the visitors for the majority of the match. Sir Alex Ferguson’s side were denied a single shot on target at the Etihad Stadium, and Mancini was convinced the victory was well earned.
"I think that we deserved to win this game," he told Sky Sports after the game.
"We scored, we had chances [and] we played well. We had a chance to score a second goal.
"I don’t think they had a chance a score. It was a good performance. It was a difficult game because United are a top team."
The Blues have to travel to Newcastle United next Sunday before facing QPR on the final weekend of the season at the Etihad Stadium.
He said: "We are happy but I think that next Sunday we’ll have another difficult game."
The former Inter Milan boss brushed off suggestions he should publicly back his team as contenders for the title now for his supporters’ sake.
The Italian added: "I don’t think that it’s important what I can say for our supporters or my players. It is important that we work well.
"We go to play Newcastle on Sunday - [Manchester United] play an easy game against Swansea.
"For this reason I don’t think it changes [anything] for us. For now, we are top of the league but I think that United have a light advantage yet."
The match began awkwardly and it looked like the players were going to head in at the break with a 0-0 scoreline until Kompany’s powerful header, shrugging off his marker Chris Smalling.
"[The goal was at] the perfect time for the first half," Mancini admitted.
"But it was important to score another goal in the second half but like this you have a risk [the opposition can equalise]."
Sir Alex Ferguson and Roberto Mancini clashed at one point in the second half when they diasgreed with a refereeing decision at the other side of the pitch.