The Bosnian forward says his first goal helped to take the pressure off the defending champions at Carrow Road but admits he did not expect to partner with Sergio Aguero.
Dzeko scored two goals in the first five minutes as City defeated the Canaries, and he thought he had bagged a hat-trick until his third strike was recorded as an own goal after hitting off the post and then the back of Norwich goalkeeper Mark Bunn.
The Bosnia & Herzegovina international has built up a reputation as a 'super-sub' and says manager Roberto Mancini gave him no indication during training that he would partner with Sergio Aguero to start the match.
"I didn't expect to play, because it looked in training that I wouldn't," Dzeko told the club's official website. "I was surprised before the game when the manager gave the team. Everyone wants to play, I was back and gave the maximum."
Dzeko's first goal came after just 85 seconds, and the 26-year-old said that finding the target early had taken a weight off his shoulders.
"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," Dzeko said.
City was reduced to 10 men after Samir Nasri was sent off following a clash with Sebastien Bassong, but Dzeko claims he was confident that his side would see the game out even with the disadvantage ont he road.
"We did it once before against West Brom, we played with 10 men for 50 or 60 minutes. We did well and we did it again here. It was difficult, but we worked hard," Dzeko said.