City have failed to progress out of the group stage in each of the past two seasons but kicked things off in a fresh and exciting manner under Manuel Pellegrini by beating Viktoria Plzen 3-0 at the Doosan Arena.
"It's the perfect start," Dzeko told Sky Sports 2. "The last two years we didn't do that in the first game and now we did.
"Especially coming away from home, we know it's always difficult to play away in the Champions League because every team is very strong and Plzen showed in the first half how they can play football.
"We're very happy to go home with the three points."