Manuel Pellegrini's men are bottom of Group E, two points adrift of second-placed Roma, ahead of Tuesday's clash against Bayern Munich.
Despite two Premier League titles in the past three seasons, City have only reached the knockout stages of Europe's premier club competition once in that time.
Nasri said there would be no more excuses for City, who need a win at home against Bayern.
"Let's be honest, with the salary of every player and the level of those players, 90 per cent of the team is world class, then not to qualify from the first round of the Champions League would be a huge blow for the club - and for us as well," the Frenchman said.
"The thing in the Champions League is not just the talent, it's not being a team, it's the experience as well.
"We need to show we are smart players and to use what happened in the last couple of years to improve. We still have a chance and we need to take it. Now is the moment."
City have suffered losses to Bayern and CSKA Moscow, who they have also drawn with along with grabbing a point against Roma.
Nasri said his side were fortunate to still have a chance of qualifying for the knockout stages.
"We are really lucky," he said.
"Normally, we'd be out, but we still have a chance. This is our chance, we have to take it. We have to play with nothing to lose.
"We need a big reaction, we need to improve. A team like us cannot go out in the first round of the Champions League. We have to win. Hopefully the fans will respond and be there for us as well."
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