The Chilean, whose side is still fighting for honors in four competitions, believes his title-chasing squad has usurped the Red Devils as the dominant force in the city.
The Chilean has engineered an assault on four competitions this season, with a Champions League last 16 tie against Barcelona the latest test standing between City and an unprecedented quadruple.
David Moyes' men, meanwhile, have struggled to defend the title they won last season, have been knocked out of both domestic cups and are fighting just to finish in the top four.
And while Pellegrini appreciates United's past glories, he is confident his side has altered the balance of power and is now a more dominant force than its city rivals.
When asked if City had overtaken the Red Devils, Pellegrini told reporters: “The biggest team is City now, but we can't forget the last few years.”
“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," he added. “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.”
Meanwhile, Pellegrini confirmed Sergio Aguero will miss Tuesday night's clash with Barcelona, though Fernandinho could overcome a muscle problem to play.
“Fernandinho has a chance to play,” the City boss said. “He is in the squad and trained well without any problems today. Sergio is not in the squad.”
“I'm sure our fans will enjoy this game. I think they have enjoyed the season and it is important we continue to play this way,” Pellegrini said.