City bowed out of the Champions League as they slipped to a 4-1 aggregate defeat to the Spanish champions with a 2-1 loss at the Nou Camp.
City did rise to the occasion and applied pressure as they sought to overturn a 2-0 first-leg deficit, but a 67th-minute strike from the brilliant Lionel Messi effectively ended their challenge.
They battled on, even after the sending off of Pablo Zabaleta in the 78th minute, but Vincent Kompany's late equaliser proved mere consolation and was immediately cancelled out by Dani Alves in the last minute.
Barca were the better side but City can take encouragement from their performance and, after premature exits at the group stage in the past two seasons, progress is being made.
France playmaker Nasri said: "I think we played a good game. I think we did everything we could.
"We can have regrets about the first leg - it is in the first leg we lost it - but here we did everything.
"I think this defeat is going to be good for us in the future.
"This is where you get experience and get much stronger as a team and a group. Next year our target is to be up there with the best."
City were aggrieved not to have been awarded a penalty in the second half when substitute Edin Dzeko was clipped by Gerard Pique.
To compound matters, Zabaleta was dismissed for taking his complaints too far in the protests that followed.
Those incidents, however, could be considered to have redressed the balance somewhat after Barca were also denied a penalty and had a goal harshly disallowed for offside in the first half.
With the red card, refereeing controversies and Barcelona goalscorers being the same, the match mirrored the first leg in many ways.
City manager Manuel Pellegrini could only watch from the stands as he began his touchline ban for his outspoken attack on the referee in Manchester last month.
Nasri said: "Once again, we did not have any help from the officials so it is a little bit difficult.
"But our only regret is we didn't play the first leg like we did here.
"In the first leg if we had attacked them from the start, pressed them like we did here we could have had better chance to go through."
City may have won the Capital One Cup earlier this month but, after Sunday's FA Cup loss to Wigan, they have now gone out of two other competitions in the past four days.
They now face a catch-up job in the Barclays Premier League having fallen nine points behind leaders Chelsea while concentrating on cup football over the past three weeks.
Nasri, 26, said: "We don't have a choice. Now our target is to win the league.
"I think here we showed we have the quality to be up there with the best teams in Europe.
"We came here to play. I don't think you are going to see that many teams come to Camp Nou and have that much possession, that many attempts on target.
"It is a good thing for us. It is important now to finish the season well and win the league."
City are back in action at Hull at midday on Saturday.
They are awaiting an update on the injury sustained by top scorer Sergio Aguero in the first half at the Nou Camp.
The Argentina striker felt a twinge in his hamstring early in the match and, having only recently returned from a five-game lay-off with problems in that muscle, was withdrawn at half-time.
Assistant manager Ruben Cousillas, who called the shots on the touchline in Pellegrini's absence, said the move was precautionary.
He said: "Apparently it is nothing serious, he felt some kind of pain in his muscle.
"It is more a precaution, but we are doing some tests to assess it.
"It will be up to the medical staff who determine the extent of the injury, so we cannot speculate about this."