Reigning champions City closed the gap at the top to 12 points with seven games to play after substitute Sergio Aguero's fine individual strike settled the derby at Old Trafford.
Mancini had insisted in the build-up to the game that City did not deserve to trail their local rivals by so many points and he was pleased with the performance as his side avenged a 3-2 home defeat by United earlier in the campaign.
"We are happy because we played very well," Mancini told Sky Sports 1. "This is the most important thing for us. We deserved to win.
"The game before against United we dominated that game and we lost in the end which I don't know how it's possible but this is football.
"Today was the same. We played very well, we deserved to win, but we conceded the goal because we didn't pay attention and didn't mark very well."
The Italian is not anticipating a late charge to retain the title and is instead happy to concentrate on securing second position in the Premier League table.
He added: "I think it was important for the second position. I think that we don't deserve to stay 15 points behind, but this is football.
"We demonstrated tonight and also in the first game when we lost that we are the same. I think we probably showed that we deserve to stay very close."
When asked about the title, Mancini replied: "It's finished.
"What is important is only for the second position. [If we finish] 15, 12, 18 points behind it doesn't change anything. I think that we are like them but they score more than us and this is the difference."