City continued their pursuit of the Premier League leaders with a 2-0 victory over Fulham on Saturday.
David Silva scored both goals as the champions secured their fourth straight win and Dzeko told the club's website: "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."
Dzeko, City's top scorer with 11 goals in all competitions this season, added: "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."