City eased into the knockout stages with their 5-2 win over CSKA Moscow on Tuesday night with two games to spare, doing so in style as Alvaro Negredo helped himself to a hat-trick.
After group stage failures the last two seasons, qualification comes as something of a relief to City, but Nasri sees no reason why they cannot kick on further when the last 16 comes around.
They could still go into the draw as top seeds as well, but they would almost certainly need to beat Bayern Munich in Germany as well as win their next home clash against Viktoria Plzen.
Nasri said: "This is something that we really have wanted to do for the past three years and we did it, so we are very happy.
"It's a big achievement for the club because this is the first time we've gone beyond the group stages, 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."