Despite cutting the deficit to Sir Alex Ferguson's side to 12 points, City's championship defence is all but arithmetically over with only seven games remaining.
Mancini, who may be without David Silva for Sunday's FA Cup semi-final owing to the hamstring injury he suffered in the second half, said: "We know that we can win the title next year. This year we did some mistakes but now we can do nothing, the season is gone.
"It is important that we continue to win – we have another seven games. For now we need to play like this. For next season we have two or three months where we can work well and where we can improve our team."
The manager is sure that the 15-point gap his side faced entering the derby will not be repeated next season. "No. I think that we showed this tonight. We can't be 15 points behind," he said before accepting that Ferguson's side deserved credit. "We can say United won a lot of games. They lost their last [league] game against Norwich a long time ago [in mid-November], so they deserve to win this title.
"This win is important for us because it can help us for second position. We deserved to win because we played better. We played good football. We didn't take any risk."
James Milner opened the scoring after 51 minutes but Vincent Kompany's own-goal levelled the match before Sergio Agüero's 78th-minute winner.
United go to Stoke City on Saturday with Ferguson aware that they could still make life awkward for themselves. "We won't be complacent," he said. "If you look at the history of this club over the years we always make it difficult for us. The supporters are hanging on the edge of their seats every year. It is a 12-point lead, we go to Stoke at the weekend and we will have a go."
Despite City dominating for long passages Ferguson felt his team were the better performers after the break. "It was a very intense game, very competitive, with two of the best teams in the country," he said.
"I thought we were the better team in the second half but we know Sergio Agüero is a fantastic finisher and we gave him a lot of room for [the winner].
"I was pleased with the second-half performance. There were a lot of pluses. Robin van Persie was fantastic and Wayne Rooney got some time on the pitch after coming back.
"Our form is good. I have no complaints. If you look at the whole thing, it's not a bad day for us in terms of the performance level. You don't want to lose a derby game but we're OK."
Mancini, whose long-term future as City manager is in the balance, can now focus on the FA Cup semi-final with Chelsea at Wembley on Sunday. "I think it will be a different game," he said. "Chelsea is in a good moment."
Regarding Silva, he said: "David [has hurt] a hamstring. Maybe it is not so bad but I don't think he will be ready for Chelsea."
Kompany believes that the momentum from the victory can ensure that City finish the season in convincing fashion. "I do believe the way we finish this season is going to have an impact on next and this is a good game to have under our belts to take into next season," the captain said.
"A derby is always a special game for us and to win this game is massive. Our fans are still celebrating and it's going to be a great night for us.
"We worked very hard. They played very offensively, they have an unbelievable strike force, so we had to close the gaps and be tight to them, which we did very well. I don't think we gave a lot of chances away and, if you look at our overall play, I thought we were the better team."
Milner said: "I thought we deserved it. It was a great result and our aim is to keep that momentum up until the end of the season.
"Regardless of where we are in the table, a derby is a derby and you always want to beat your rivals, and that's the case every game."
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