Manuel Pellegrini's men booked their place in the last 16 on Tuesday with a 5-2 victory over CSKA Moscow, going through alongside Group D leaders and defending champions Bayern Munich.
City had failed to qualify for the knockout phase in their previous two seasons in the competition under Roberto Mancini.
And Nasri feels the Etihad Stadium club have time to improve before the next round gets under way in February.
"It's a big achievement for the club because this is the first time we've gone beyond the group stages," he said. "But there is still a long way to go.
"A club like Manchester City isn't just going to be happy reaching the last 16. We want to get as far as we possibly can in this competition.
"As a team we've progressed and, even if the past two seasons have been tough and we've had difficult groups, if we work as a team, we have time to get better and better because the next round isn't until February.
"There are some important teams in Europe but I think we have a strong squad and we'll see where we can go in this Champions League."
City next face basement club Viktoria Plzen at home on November 27.
