"It demonstrated tonight [Monday] that we are not (15 points worse)," he said.
"We are happy, it is normal, you play football, we are happy because we won. We play football to win.
"Every time we play United...also the game at the Etihad, we dominated and lost, but this is possible, it is football.
"We wanted to play football, we had the ball, kept it and played better. It was important for us, we showed we didn`t deserve to stay 15 points behind."
When asked if the result could affect United's confidence ahead of their final seven games, Mancini said: "United? No. The championship is finished.
"But we deserved to win because we played better, we played good football. We didn't take any risk."
For Mancini, the remaining Premier League fixtures are all about securing second place and, with that in mind, Mancini was especially pleased with the win.
The Italian said: "This is important for us because we can get second position.
"Maybe we have one game in hand and if we win the game against Wigan we go 10 points in front of Tottenham.
"After that maybe we don't have a problem.
"This is for our supporters because they deserve this victory. After being 15 points behind it was important for them."
Of some concern for City was the loss of playmaker David Silva in the closing stages of the game with a hamstring injury.
The Spaniard now looks doubtful for Sunday's FA Cup semi-final at Wembley.
Mancini said: "Maybe it is not so bad but I don't think he will be ready for Chelsea."
Mancini will now begin his preparations for the Chelsea clash as he targets a second cup final appearance in three years.
He said: "I think it will be a different game, it is a semi-final.
"Chelsea are in a good moment, they play well and it will be difficult.
"It will be a good game, probably, but it will be different. Semi-finals are different from championship games."
While winning the FA Cup would bring City handsome consolation after their apparent failure to defend the title, a review of why they have failed to achieve their prime objectives will still be undertaken.
Mancini feels City proved with their defeat of United they are capable of challenging for title glory again next season.
Mancini said: "We need to continue to play like this for next season.
"We have two or three months where we can work well, where we can improve our team.
"I think we showed tonight we can't be 15 points behind.
"But we can say United won a lot of games. They lost their last game against Norwich a long time ago and they deserve to win this title, for sure."
Mancini was bemused by a recent report suggesting he had been to Abu Dhabi to meet with the club's owners.
He said: "I was on there holiday, I didn't train for 10 days.
"People who said this are very stupid. This was a personal situation."
James Milner hopes City`s win at United on Monday will stand them in good stead for the rest of the season.
Milner's goal was the first in City`s 2-1 win which, while good for local bragging rights, does little to improve his side's chances of retaining their title.
United lead the way by 12 points with seven games left, although City remain alive in the FA Cup.
They play Chelsea in the semi-finals this weekend and Milner wants to get some momentum going.
"Every derby is a massive one, we wanted to come and put in a performance," he told Sky Sports 1.
"We deserved the win at what is always a tough place to come. It was a great result and we will want to keep the momentum until the end of the season.
"We worked very hard and got a win. United are tough to break down at Old Trafford where they have an excellent record."
City skipper Vincent Kompany was in the wrong place at the wrong time when Phil Jones' header went in off him in the wake of Milner`s goal, but a Sergio Aguero special won it for the visitors.
Kompany knows the win will do little in the current title race, but hopes it can make a difference heading into next season.
"We worked very hard and we gave them few chances," he said.
"We were the better team. Every game we play to win and the way we finish the season can have an impact on the next when we will start from the beginning.
"This is a good game to have under our belt."