The champions continued their pursuit of city rivals United as they eased to a fourth consecutive win against Fulham, with a brace from David Silva ending in a 2-0 victory at the Etihad.
Since losing to Alex Ferguson's side at the end of last year, City have recovered their poise and Dzeko says they are not going to give up without a fight.
Speaking to the club's official website, he said: "We have to just keep doing what we're doing.
"I think Manchester United will drop points sooner or later but we just need to keep winning and keep the pressure on them."
City were dominant throughout and the Bosnian was not short of opportunities although failing to convert.
Dzeko, City's top scorer with 11 goals in all competitions this season, said: "David took his goals really well and he is disappointed he didn't maybe get a third, but I'm really pleased for him and that the team won.
"We are a bit disappointed we didn't score more goals after taking the lead so early in the game and I think if we'd scored again in the first half we'd have gone on and won by more but sometimes it doesn't pan out like that.
"We got the second at a good time so we have to be happy.
"I'm disappointed I didn't score, but I think I played okay. As long as we keep winning, I'm happy."
Silva had scored only one goal previously this season and his recent return to form has given City a lift.
The Spaniard added: "It was great to get two goals and I had the opportunity for a third, for the hat-trick, but I didn't make contact as good as I wanted. But it is the points for the team that really matter.
"It was a good game, the important thing was to get three points and put some pressure on United."