The Bosnian accepts City were not at their best as they surrendered two potentially vital points in a frustrating 3-3 draw with Sunderland at the Etihad Stadium on Saturday.
That result - which would have been worse but for two late City goals - has given rivals Manchester United the opportunity to move five points clear at the top on Monday but Dzeko will not give up the chase.
The 25-year-old said: "There are seven games to play, and the way we dropped points, United can drop points as well, so everything is still open.
"We need to go from game to game and try to win every match.
"The next is Arsenal. We will play to win and then we will see.
"They are fighting for a Champions League place and are a top team, so it won't be easy. It should be a good, open game.
"Maybe we thought Saturday was going to be easy. We had won all our home games so maybe we thought we could count on all three points - but it's not like that, and you have to fight for every point."
Having led the table for most of the season, City are now need favours from other teams to get them back into the race.
City trail by two points with seven matches remaining, one fewer than United, who play their game in hand at relegation-threatened Blackburn.
Dzeko said: "It is an important game for Blackburn as well so everything is possible.
"We lost points on Saturday, and they could drop them at Blackburn or somewhere else."
Dzeko was at the centre of controversy on Saturday over the penalty which led to City's first equaliser.
Sunderland's players complained Dzeko had dived to win the spot-kick but the City forward was insistent he had been fouled by Craig Gardner.
"It was a penalty - I still have pain in my leg," said Dzeko, who became involved in an argument with Sunderland defender Phil Bardsley over the matter after a later stoppage in play.
On that, Dzeko said: "One guy pushed me away and said, 'Why are you cheating?'
"So I asked him what he was talking about and said it was a penalty. That's why I was angry.
"He said I was cheating. He can say what he wants, but should never touch me.
"Mario [Balotelli] told me to stay calm, but I was calm - they can't push me and touch me that way."