City have emerged from the shadow of United and have the chance to do the double over them with victory at Old Trafford tonight.
But Pellegrini has been keen to pay due respect to United ahead of the clash, insisting they must progress further in order to establish themselves as a major force on a consistent basis.
"I think this club has been trying to work in the last four years to reduce the difference we have against important teams - against Manchester United, Chelsea and Arsenal, and in Europe as well," he said.
"It is always important because when you have two important teams from the same city you always want to be the best team.
"But we are not just fighting against Manchester United and in some ways it doesn't matter."
The Chilean was also keen to explain previous comments where he appeared to suggest City were now the dominant force in Manchester.
"It was easy because I meant in this season, the best team is Manchester City because we were top of the table," he added.
"But at the same moment I said we must recognise what Manchester United have done in the last 20 years.
"Of course all the other clubs expected United would be in the top positions in the table (this season), but for different reasons at this time they are not. But they continue to be a difficult team.
"It is difficult because for so many years the same person managed a team with his ideas.
"It is difficult to analyse without knowing it from the inside - but it was always going to be difficult to replace (Sir) Alex Ferguson."
As for tonight's game, Pellegrini says form will go out of the window, despite his side holding a 12-point advantage over their city rivals.
A victory at Old Trafford will aid their quest for a second Premier League title in three years.
But Pellegrini, whose first taste of the Manchester derby brought a thumping 4-1 win at the Etihad Stadium in September, has moved to play down the suggestion that the balance of power is shifting to the blue half of the city.
"I don't think we are favourites in any game," he said.
"We are in a good moment but we are playing against a big team in their own stadium, so I don't think we are the favourites.
"Of course we always expect to go and win every game but, I repeat, just because Manchester United have had a difficult season it does not mean we are going to win.
"We have to go there and play a very good game."
City sit six points behind Premier League leaders Chelsea with three games in hand, and Pellegrini will have captain Vincent Kompany back to bolster his defence at Old Trafford.
United go into the derby in good spirits on the back of successive wins over Olympiakos and West Ham, but Pellegrini also believes his side's torrid week against Wigan and Barcelona earlier this month could stand his own side in good stead.
"All of us want to stay in every competition but when you are eliminated one of the positive things - if you can find a positive thing - is that we are now just focusing on the Premier League," added Pellegrini.
"You don't have problems in that sense, mentally or physically. We are just trying to fight for the title.
"I know we must go game by game and we just have to win on Tuesday and then at Arsenal on Saturday after that."
Watch Manchester United v Manchester City live on Sky Sports 1 and Sky 3D from 7pm tonight.