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.
"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."