The reigning champions launched their defence with a hard-fought 2-0 victory at Newcastle on Sunday with an efficient, rather than dazzling, display.
Dzeko told CityTV: "It's just the beginning of the season and it will be, definitely, a long season with the five teams fighting for the title. This is just the beginning.
"It's good to start with a win, but we are not there. There are so many games to come and we have to prepare for the next one, for the big game against Liverpool to try to win at home.
"We have brought in some great new players. Some of them still need time because it was the World Cup and a lot of us came later to the pre-season.
"I think we can still improve a lot. Each game, we can be better and better and just try to continue where we finished [at Newcastle]."
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