Dzeko scored two goals in the first five minutes as City defeated the Canaries and thought he had bagged a hat-trick until his third strike was recorded as an own goal against goalkeeper Mark Bunn.
The Bosnia 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 Sergio Aguero.
"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," he added.
City were reduced to ten 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.
"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," he reflected.