The Manchester City boss saw his side run out 3-0 victors at Old Trafford with Edin Dzeko scoring twice and Yaya Toure on target, while Joe Hart went relatively untested
City opened the scoring just 43 seconds into the game as Edin Dzeko followed up to tap home from close range after Samir Nasri hit the post.
Dzeko scored a second after the interval before Yaya Toure wrapped up the comprehensive win in stoppage time, much to the delight of the Chilean.
"I think that we did a really good performance," Pellegrini told Sky Sports. "We scored three goals, we had three or four more clear chances to score.
"I don’t remember a clear chance United had. We were a compact team, an aggressive team from the beginning.
"For me, it’s very important to keep our clean sheet. We know we can score a lot of goals but today we were very compact as a team.
"I think we were complete in attacking and defending."
Pellegrini also believes the derby victory will give his side a psychological boost in the title race, having moved three points behind Chelsea with two games in hand.
He added: "It was very important psychologically for us. We had to play away against a great team like Manchester United.
"It’s important we continue recovering points against Liverpool and Chelsea. We are four points up from Arsenal. It's important to keep adding points."