The Chilean oversaw a huge win against fellow derby debutant David Moyes at the Etihad Stadium on Sunday, with City laying down an early marker in their bid to reclaim the Premier League title from local rivals United.
But, while Pellegrini conceded that the emphatic nature of the scoreline was a surprise, he was keen to attribute that to his players' performance rather than any failures on United's part.
"It was a very important result. Normally you don't expect to win 4-1 to Manchester United but the most important thing is the way we played and I'm very happy," he said.
"Normally, derbies are more equal but today we had a very good day and that allowed us to have the superiority.
"Maybe (United) couldn't play better because we played very well. We had good possession, we tried from the beginning to make space and we did it.
"I also think that in defence we played well, we didn't give them space to do damage."
The former Real Madrid boss also insisted that his charges can get even better under his guidance as they adapt to his style of play over time.
"I would be very happy if we win all the games 4-1, we wouldn't need to improve!" he enthused.
"But I think we must improve every day. Not every game is the same, we don't have the same day. We are just starting another style, another way to play, and I hope we will improve."
Manchester City sit third in the Premier League after Sunday's win, two points behind north London duo Arsenal and Tottenham.
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