The 1-0 win over Manchester United at the Etihad Stadium on Monday means City will secure their first championship since 1968 if they win their final two games, at Newcastle on Sunday and at home to QPR seven days later.
Yet Mancini still insists United are favourites and does not want his players to get lulled into a false sense of security, saying: "It is not finished. If we think it is finished, we will be making a big mistake. United are the favourites."
He said United have "easy games" in the run-in, playing Swansea and Sunderland.
In comparison, he added: "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."
Pop superstar and celebrity City fan Liam Gallagher was less cautious as he burst into the media room after Mancini had given his post-match observations to announce: "Ferguson must have been on the whisky" and: "I love Mancini, he is nearly as cool as me."
Mancini might have appreciated the plaudits but he was happy to praise his team, believing their victory was fully deserved because of their attacking attitude towards the game. "We played better. We deserved to win but it was difficult because they had all the players behind the ball."
Meanwhile, Alex Ferguson was unhappy about a challenge by Nigel De Jong on Danny Welbeck, and the manner in which Mancini was talking to fourth official Mike Jones.
The second-half incident sparked a furious touchline row between the two managers, and Jones stood between the pair at one point to prevent it spilling over before they were eventually pulled apart by members of their respective backroom teams.
"He (Mancini) refereed the game," said Ferguson. He was out on that touchline the whole game haranguing the referee, the fourth official and the linesmen. The minute I come off the bench for a bad tackle by De Jong on Welbeck, he was out again. He can't have it both ways. He's been complaining about referees this season but he won't be complaining tonight that's for sure."