The Chilean watched his team demolish United at the Etihad Stadium, with Sergio Aguero scoring twice and Yaya Toure and Samir Nasri also registering.
"I'm very happy. Before the match, I say we always enjoy the derby but if we win, we enjoy double," Pellegrini told Sky Sports.
"The way we played, I want this team to play the whole year. It was very similar to how we played against Newcastle, we try to play in the same way. It doesn't matter who we are playing, or the score during the match.
"We scored four goals, and Manchester United didn't have a clear chance - though I say it was a beautiful free-kick from Rooney.
"We are a very aggressive team, with or without the ball, and we have an important security in defence also."
Pellegrini was pleased with the high tempo his team displayed.
"All the teams want to play quickly, but you must have the technique to do it," he added. "We have the players to do it.
"This was a high test today. Against Newcastle, I think we also played really well. We're just starting the season, we must continue improving in a lot of things, but this game will be important for confidence and trust in the whole team.
"We play today the way we work the whole week. That for me is very important. That signifies the players are trusting in what we are doing."