Mancini, who celebrated the third anniversary of his appointment this week, has restored City to trophy-winning glory after a generation without success. City ended a 35-year wait for silverware by winning the FA Cup in 2011 and followed up by claiming the Barclays Premier League title in dramatic fashion last season.
Mancini has benefited from the wealth of the club's Abu Dhabi-based owners but he feels he is ahead of schedule. The 48-year-old said: "I think that we worked really well because when I arrived here three years ago I didn't think that maybe in two years we would win the Premier League, FA Cup."
He added: "I thought that maybe four or five years to win the Premier League because it isn't easy. We changed things in England, and Manchester in particular, because for 20 or 30 years United won everything.
"We changed this situation because we did well. We've also made mistakes, which is normal when we work and it can happen, and we need to continue to work hard to improve our game."
Mancini's City career has become entwined with that of striker Mario Balotelli, his former Inter Milan protege. Balotelli, signed from Inter for £24million in 2010, has been backed repeatedly by Mancini despite numerous controversies on and off the field.
There has been considerable speculation this season the enigmatic forward could leave City in January and that intensified this week when it emerged he was taking the club to a Premier League tribunal.
The 22-year-old was contesting a fine of two weeks' wages imposed by the club for his poor on-field disciplinary record last season but he dropped his challenge on the morning of the scheduled hearing. Mancini recently voiced concerns Balotelli's talent could go to waste if his attitude does not improve but he appears intent on backing his player.
Mancini said: "I am his manager, like other players, and if he deserves to have other chances he will have them." A statement from the club said Balotelli abandoned his appeal partly out of respect for Mancini but the manager is pleased the striker showed respect for his own reputation.
Mancini added: "This is an old situation and it is normal when someone does a mistake he should take his responsibilities and Mario did this. It's normal. He (should) respect himself, not me, because it's important for him to respect himself, very important."