Questions were being asked of City's trophy-winning credentials after they slipped to a third Barclays Premier League defeat of the season at Chelsea just over a week ago.
Nasri feels they have now been answered after a 7-0 hammering of Norwich on Saturday and Tuesday's classy 5-2 demolition of CSKA Moscow.
The defeat of the Russians at the Etihad Stadium means City now cannot be caught in second in Champions League Group D and will play in the knockout stages for the first time in February.
After failing to get out of the group in the past two seasons, that marks the next significant step in the club's progression but nobody at Eastlands wants it to end there.
Nasri said: "I am really happy. It was one of the targets for the club at the start of the season to go through in the Champions League, as for the last two seasons we didn't do it and were really disappointed.
"But it's just a start because a club like Manchester City should go really far in the Champions League, and we now have time to progress as a team and be even better, because the last 16 doesn't start until February.
"We were really pleased with the performance. There was some stuff we could have done better as a team to avoid the two goals, but it was a good performance with a lot of chances.
"In two games we have scored 12 goals, so now we focus on Sunderland.
"Since the start of the season we have struggled a little bit away but now we are starting to show the real face of Manchester City."
Nasri was outstanding as City carried on where they left off against Norwich to demolish the Russian champions.
But the main headlines were stolen by hat-trick star Alvaro Negredo and strike partner 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, both of which highlighted defensive concerns.
Doumbia eased round Costel Pantilimon - again preferred to England's Joe Hart in goal - for the first after a defence-splitting pass from Pontus Wernbloom on the stroke of half-time.
Again inspirational captain Vincent Kompany was sorely missed as the Russians found the gap.
Doumbia's second came from a penalty on 71 minutes after the Ivory Coast international had beaten, but then been clumsily brought down by, Gael Clichy.
But the result had not been in doubt since Aguero scored his first from the spot after three minutes and City raced into a 3-0 lead inside half an hour.
Aguero's second came after he received a fine pass from Nasri and wrong-footed the defence with a deft touch and turn. He then teed up Negredo to put City in command.
Reaching the last 16 was one of the minimum requirements for new manager Manuel Pellegrini this season and Nasri feels the squad have been reinvigorated by the Chilean.
He said: "Everyone played with lots of confidence and we have a manager who tells us what is good and what is bad, so we've moved on as individuals and as a team.
"Everyone in the dressing room is really happy because we did what we wanted at the start of the game, which was to go through, and to qualify with two games left in the group stage."
Nasri certainly appears to be revelling in life under Pellegrini after struggling last term and having apparent difficulties with former boss Roberto Mancini.
The 26-year-old said: "I have felt good since the start of the season.
"On the first day I had a good talk with the manager and I said I wanted to have a great season because last year I struggled after the Euros, and that wasn't the real me.
"I worked hard in pre-season to find my real form and I am happy that I am performing.
"I feel loved and I'm trying my best each time I go out so it's all positive."
The downside for City was that midfielders David Silva and Fernandinho both had to be withdrawn as precautionary measures.
Spanish playmaker Silva was due to appear at a press event in London for a Gran Canaria holiday company on Wednesday but pulled out to undergo assessment in Manchester.
Pellegrini said after the game: "David Silva and Fernandinho both had to be substituted because they had small problems. We will see tomorrow with the doctor."
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