City had made an indifferent start to the season, dropping points at Cardiff and Stoke in recent weeks.
However, the 2012 Premier League champions blew away United with goals from Samir Nasri, Yaya Toure and a brace from striker Sergio Aguero – before a late Wayne Rooney consolation – in a devastating display to the delight of Pellegrini, whose side climbed to third in the Premier League.
“I’m very happy. The way we played is the way I want this team to play, very similar to against Newcastle [4-0 win],” he said. “We played the way we work all week.
“We went 4-0 up and Manchester United didn’t have a really clear chance apart from a beautiful free-kick by Rooney and one corner.
“We have been playing irregular in other games, but it is normal in this moment of the season.
“This was a high test and the players had a great answer.”