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 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 and 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."
City take on bottom side Reading at the Etihad Stadium hoping to follow up last weekend's impressive 3-1 win at Newcastle.
Reading have won just one of their opening 17 games and face a tough battle to avoid relegation but Mancini is not complacent.
He said: "We're playing against a team like Reading with only nine points and people say they will be relegated, but it will be a difficult game.
"I watched them against Everton - when they beat Everton - and against United when they lost 4-3.
"Up front they are very strong. Maybe they concede goals but we need to play like against Newcastle if we want to win the game."
The victory at Newcastle was a strong response by City after having their unbeaten record ended by rivals Manchester United the previous week.
Mancini, whose side still trail United by six points at the top of the table, said: "It was important because it was a tough game.
"Newcastle is usually difficult. After our performance against United I was sure we would play a good game against Newcastle.
"I didn't know if we could win or not but I think we played very well."
City hope captain Vincent Kompany can prove his fitness after a groin injury to return while midfielder James Milner is also available after a hamstring problem.
Forward Samir Nasri has been ruled out of the Royals clash and the Boxing Day trip to Sunderland with a groin injury and defender Aleksandar Kolarov (knee) is also missing this weekend.
With five games in the next 15 days, Mancini expects to have to make changes.
He said: "When you play every three days it's impossible to play with the same players and you need to rotate."