City secured a place in the last 16 of Europe's elite competition for the first time - and with two games to spare - as they crushed CSKA Moscow 5-2 at the Etihad Stadium.
After failures at the group stages in each of the past two seasons it was an achievement that marked the next significant step in the club's development.
Yet while City are pleased with their progress, Nasri is already looking forward in hope of going deeper into the competition when the knockout rounds start.
The Frenchman 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."
Nasri was outstanding as City carried on where they left off after Saturday's 7-0 thrashing of Norwich to demolish the Russian champions.
But the main headlines were stolen by hat-trick star Alvaro Negredo and Sergio Aguero, who took his tally for the season to 13 with another two goals.
City's flow was twice interrupted by goals from Seydou Doumbia - the second a penalty and both highlighting defensive concerns - but the result was never in doubt after Aguero claimed his first from the spot after three minutes.
City were taught a lesson by Bayern Munich earlier in their campaign but have won their other three Group D matches comfortably and manager Manuel Pellegrini believes they can now challenge any side.
Asked if City could beat anybody, Pellegrini said: "I think so but, at this level, also every team can beat us.
"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."