The Bosnian forward, who opened the scoring inside the first minute at Old Trafford, believes that City's fast start made it difficult for their rivals to compete with them.
"We just wanted to start from the first minute to press them high and score an early goal which we did," Dzeko told Sky Sports News. "Then it was all about us. We scored another two in the second half so we have to be happy.
"This game was very important for us. Now we are only three points behind Chelsea and this can be crucial at the end of the season."
City are now three points behind leaders Chelsea with two games in hand.