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.
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And while Pellegrini appreciates United's past glories, he is confident his side have altered the balance of power and are now a more dominant force than their 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.”
He added: “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.”
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Meanwhile, Pellegrini confirmed that 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,” added the City boss. “He is in the squad and trained well without any problems today. Sergio is not in the squad.”
He added: “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.”