Dzeko scored twice on a rollercoaster afternoon at Carrow Road, and thought he had a third but his breakaway effort on 67 minutes has been officially credited as an own-goal after the ball bounced off the post and the back of Norwich keeper Mark Bunn before rolling into the net.
And the Bosnia striker admits that he was surprised to start the game, as boss Roberto Mancini had given him no hint of it in training in the run up to the match.
"I didn't expect to play because it looked in training that I wouldn't. I was surprised before the game when the manager gave the team," Dzeko told the club's official website.
"Everyone wants to play, I was back and gave the maximum."
He scored the opening goal just 85 seconds into the match to give the champions the perfect start.
"Maybe it's important to score the first chance, it's different when you're winning 1-0 - maybe it's easier when you're a goal ahead and then we got the second soon after," he said.
And he said he was not worried when Samir Nasri was sent off in the first half.
"We did it once before against West Brom, we played with ten men for 50 or 60 minutes - we did well and we did it again here - it was difficult, but we worked hard."