City were the weaker side in the opening 20 minutes and it appeared as if they would surprisingly be overwhelmed at their own stadium.
Mancini's men rallied, however, as United failed to produce a decent attacking opportunity and as the players, backed by thousands of fans, achieved better control of the ball, they were able to string together shots more often.
The Italian manager believes that his opposing counterpart might have told his players that he would be happy if they earned a draw instead of going for the jugular and grabbing a win.
"The key was that we wanted to win and they wanted a draw," the Italian explained after the game. United failed to muster a single shot on target in the game.
"This is the difference. We deserved to win but it was difficult as they had so many behind the ball.
"Every manager can choose his team and for them it was important to play for a draw. With a draw, they knew the championship was finished."
Mancini remained downbeat about his side's chances of winning the title as he always has been in the past few weeks. He insisted that United remain favourites and confessed that he would only celebrate at the end of the season.
"It was an important result. Now we have it in our hands," he agreed.
"It is important we are top now but it is more important to be top on May 13."
City captain Vincent Kompany, who scored the winner, revealed as well that chairman Khaldoon Al Mubara made an appearance in the dressing room before the game.
The defender said: "He had a word with us. He said no matter the result he was proud us.
"We've done incredibly this season and we are building for the future."
Joe Hart hailed the tremendous support that his players received in the game. He believes the singing fans wearing blue jerseys created an intense atmosphere which only added to the tension created by the media in the buildup to the game. But he knew that his side would not let it all get to them and focus on the job during the 90 minutes.
"You could feel the intensity, everyone in the stadium could," the England custodian said.
"There has been a lot of build-up for weeks outside the team, we concentrated on what we wanted to do.
"We've not been great sometimes but we are on a good run at the moment and played a very good side there and beat them."
His team-mates will now turn his attention to their next game against Newcastle and he knows that the northern side, who are chasing a Champions League-qualifying spot, will not be easy opponents even if they lost 4-0 to Wigan in their last game.
"It's a great to win but Newcastle is now our focus.
"They are pumping themselves up in the league and St James' Park is going to be tough.
"We are looking forward to taking a good crowd there and getting one game closer."