The City boss and his United counterpart David Moyes will both have their first involvement in the fixture at the Etihad Stadium on Sunday.
But any claims that the Chilean has little idea of the fierce rivalry in the city have been played down by Pellegrini, who described the clash as a six-pointer despite being so early in the season.
"I don't need to be here to know just how important this game is to everyone," he said.
"I'm well aware. Football in England is different, I hope everyone enjoys it. It's a six-point game, these are two of the teams that will challenge.
"It's important not to be under too much pressure. David Moyes will be feeling some pressure after taking over from Sir Alex Ferguson, but some pressure is good.
"Yes, I know he had a good record with Everton against City. But with Villarreal I have a good record against him."
City have an identical record to United after taking seven points from their opening four games, the only surprise being a 3-2 defeat by newly-promoted Cardiff.
Pellegrini added: "We have had a good start, but not as good as we want. We must improve every game, it's difficult to change our style and the way we play, but winning makes you improve and we need to improve many things."
City midfielder David Silva has returned to training after a thigh strain, while defender Micah Richards is also close to returning from a hamstring problem, although Pellegrini does not expect either to start on Sunday.
"David Silva and Micah Richards are both back in training but Sunday is likely to come too soon for either to be involved in the squad," said the City boss.
But Vincent Kompany is expected to start after coming through the Champions League win over Viktoria Plzen with no reaction to his groin injury.
Pellegrini said: "I think Vincent is a very important player for us.
"We worked well without Kompany. If you see our numbers in games he didn't play, we had three clean sheets, but he is always important. He gives confidence to the whole team."
Watch the Manchester derby live on Ford Super Sunday, coverage starting at 12.30pm on Sky Sports 1 HD