City edged their crunch meeting with United at the Etihad Stadium on Monday night thanks to Vincent Kompany's headed goal in the final moments of the first half.
That result ensured City lead at the summit on goal difference with two games of the season remaining, but, in spite of having their fate in their own hands, Mancini is wary of complacency.
"It is not finished," the Italian said. "If we think it is finished, we will be making a big mistake. United are the favourites.
"They have easy games. They play against Swansea and Sunderland. We have two strong games, Newcastle and QPR. One plays for the Champions League, the other for relegation.
"It is important that we are on the top now but it is more important to be there after May 13."
United failed to muster a shot on target during the match, leading to suggestions Sir Alex Ferguson's side were overly negative in their tactics.
Mancini said: "It was important for them to play for a draw because the championship would have been finished. We played better. We deserved to win but it was difficult because they had all the players behind the ball."
Of a topsy-turvy battle for the title, in which City only recently trailed the Red Devils by eight points, Mancini added: "Football is crazy.
"It is important to always believe in yourself when you have a bad moment. We were on the top for 28 games and I think we deserve another chance.
"But in two games, anything can happen. It is enough for my players that they remember six weeks ago and we were four points ahead of United. In two games we lost everything. Up to now, we have done nothing."