Barcelona edged out City 2-1 at the Nou Camp on Wednesday night to progress 4-1 on aggregate thanks to goals from Lionel Messi and Dani Alves with Vincent Kompany finding the net for City.
Former Arsenal captain Fabregas admitted City made it hard for Barcelona and he was delighted to see Barcelona get back to winning ways after a recent poor run of form in La Liga.
"It was a very tight game. I think we were playing against a world-class team," Fabregas told Sky Sports 1HD.
"We knew it was going to be difficult, but I think it was a great result to win 2-0 over there because it is never easy to go to Manchester and win the way we did it and today was tough.
"I think we created a lot of chances; apparently there was a penalty not awarded and the goal for Neymar in the first half was onside but we take a lot of positives.
"I think we played much better than the last few games, we were not at our best and today is a way as well to lift the spirit of the team.
"We go home happy. The last couple of games we could not have said that because we were not happy going back home after some negative results but I think we played a good game today against a class team, a top team and we have to be proud of it."
Asked about Manchester's City appeal for a penalty when Edin Dzeko appeared to be brought down by Gerard Pique, Fabregas added Barcelona should have had one in the first half when Joleon Lescott caught Messi inside the box - feeling both decisions cancelled each other out
"Yeah maybe we had one too in the first half, 1-1," noted Fabregas.
Asked about Barcelona's chances of going all the way in the Champions League, Fabregas admitted it would be tough with the standard of teams in the quarter finals.
"When you play for Barcelona the minimum is to reach the final. We know it's difficult because there are some top teams like likes Bayern Munich, Atletico Madrid, Real Madrid Chelsea so it is going to be really difficult," he said.
"But a lot of people didn't expect us to go through this time against Manchester City, we did so it is a good way to keep going
"Everything is good at the club. We are in the final of the cup, we are four points behind in the league and in the last eight of the Champions League. A lot of teams would swap!"