City's 3-0 win at Old Trafford means they have kept clean sheets in their last five Premier League games, the first time they have the achieved the feat in the top flight since 1915.
Pellegrini believes his side's defensive stability is the most important asset in their pursuit of a second league title in three seasons.
"For me it's very important to keep our clean sheet. We know we can score lots of goals," he told Sky Sports. "We were very compact and worked completely in attacking and defending.
"I'm very happy with the way we're defending, now we have five clean sheets in a row (in the league)."
City were dominant against a toothless United side who have now lost 10 league games in a season for the first time since 1991 as they look set to record their lowest points total in a Premier League campaign.
City striker Edin Dzeko scored twice, the first after 43 seconds, and Yaya Toure added a late third as City won their third straight game at United's ground and Pellegrini said the margin of victory could have been even greater.
"We scored three goals and had three or four more good chances to score. I don't remember many chances Manchester United had to score," said the City boss.
"We were a compact team, an aggressive team. We started for the three points from the first minute."
City are now three points behind leaders Chelsea with two games in hand and the 60-year-old Chilean is confident his side are capable of overhauling the Blues.
"It's important at the beginning of the season to have the squad you think we will need. We have to play so many matches, it's very important to have so many strikers, but I repeat I am very happy about our defending. We are a very balanced team at the moment.
"It is important to continue adding points. We must continue playing the way we did today," he added before their visit to fourth-placed Arsenal on Saturday.
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