The Blues boss was asked about the strengths of both clubs as he prepared his side for first leg of their Champions League last-16 tie against Barcelona.
City head into the clash at the Etihad Stadium still in contention in four competitions, while traditional powerhouses United have endured a difficult campaign.
The Chilean, speaking at his pre-match press conference, said: "If we only consider this season, there is just one club in Manchester and it's ours, but you cannot forget what United has done in the previous years.
"We are aiming to keep growing by winning many trophies, not just national but international trophies.
"We are fighting for four titles this year.
"We have to be patient because you cannot change the team from one day to another.
"We have to keep the philosophy of the style and for that you need time."
City's title ambitions suffered a knock as they were beaten by Chelsea a fortnight ago and were then held to a goalless draw at Norwich.
But they restored confidence by turning the tables on Chelsea to reach the quarter-finals of the FA Cup last weekend.
That cup win also provided vindication for Pellegrini after vowing to stick to his attacking principles.
He now intends to do the same as Barcelona visit Eastlands, despite Barca's fearsome reputation.
He said: "Of course when you play against Barcelona, against an important team, you must always consider important things - but the most important thing is to try to be the same team you see every week in the Premier League.
"It is important to continue having the same style of play and the personality to try to beat Barcelona."
City are lifted by the potential return of midfielder Fernandinho after a fortnight out with a muscle strain.
The Brazilian has trained ahead of the match and looks set to resume his impressive midfield partnership with Yaya Toure.
Toure's performances in Fernandinho's absence were the subject of scrutiny but Pellegrini feels any criticism was unfair.
He said: "Yaya is a very important player for us.
"I have listened to some questions about the way he plays and Yaya plays the way I want him to play.
"He stayed only defending against Norwich because we did not have another defensive midfielder, but I think we lost an important midfielder attacking. He scores a lot of goals and gives a lot of creativity to our team.
"Playing with Javi Garcia or Fernandinho is the way I want him to play, so he is free and can give us a lot of offensive moments.
"But he knows also he has to defend and he can do it without any problems."
On the downside for City, top scorer Sergio Aguero remains on the sidelines with a hamstring injury.
That also deprives fans of the chance to see him line up against his illustrious Argentina team-mate Lionel Messi, who has shown signs of rediscovering his best after an injury-hit season.
Pellegrini said: "Without doubt it is very difficult (to stop) Messi because he is a top player of the world.
"He does a lot of different things. He has speed, good control, a good finish.
"He is a good player but I don't think Barcelona is Messi. You can have Messi tight and other players will decide the game.
"It is important to play as a team defending and attacking."
City have qualified for the knockout stages for the first time after two previous failures at the group stage.
The encounter therefore represents another important landmark in the club's continuing development and that is something Pellegrini acknowledges, although he hopes there are even bigger games to come.
Pellegrini, whose side also contest the Capital One Cup final next month, said: "It is a good test, it is important.
"I don't think it is the most important thing because we are just in the round of 16.
"We can beat Barcelona and maybe in the next round you can have a defeat.
"This club is trying to develop in all areas and so far we have a good season, but we must finish that way.
"One of our targets is to try to continue in the Champions League knowing we play against the most important club in the world."