City, who lead the Barclays Premier League on goal difference from Manchester United, need to match their rivals' result in the final round of games this Sunday to secure the crown.
City trailed United by eight points a month ago, but Toure says Mancini never lost belief, even though he publicly declared the race over.
The Ivory Coast midfielder told Sky Sports News: "Full credit to Mancini - unbelievable boss.
"He always believes in us and always tells us, 'Guys you have to believe in yourselves, Man Utd can drop some points. The most important (thing is) you have to keep winning games and United can drop some points. If they do it could be enough for us'."
Yet Toure, who scored both goals in last weekend's crucial 2-0 win at Newcastle, knows the celebrations cannot begin yet.
City host QPR, managed by their former boss Mark Hughes, at the Etihad Stadium in their last game.
Toure said: "The job is not done yet. We have to keep going and look after Sunday.
"It would be amazing. It is for that I came to City, to make history, and I hope I will make history in the next week.
"But we know it is going to be tough against QPR because they need the points."