The midfielder has lashed out at those who have suggested the Catalans are no longer the force of previous years
The first leg of the last-16 tie at the Etihad Stadium was finely poised until the 54th minute when City defender Martin Demichelis hauled down Lionel Messi with the Argentine through on goal.
Although initial contact may have been outside the area, referee Jonas Eriksson awarded a penalty and issued Demichelis with a red card, with Messi converting the penalty and Dani Alves adding a late second.
Barca have been criticised of late for some below-par performances - former Real Madrid boss Mourinho claimed earlier this week they were the "worst Barcelona for many, many years" - but Fabregas was quick to focus on the positives.
The former Arsenal midfielder told ITV: "We are top of the league, we had a great result tonight, we are in the final of the cup and there's nothing else you can ask for but the fans in Spain, in general… they put so much pressure on you as a team. That's what makes everyone feel so special to this team.
"Maybe we had to prove a point in a way and I think we did it, in style. But I think this team has done so much, has won so much but today was one of those days.
"Everyone was saying Barcelona was not the same Barcelona, some people have been talking a bit too much and as usual now they will have to shut up for a few days.”
Fabregas was adamant the tie was not yet over, however, and that Gerardo Martino's men will not take their foot off the gas in the second leg at Camp Nou.
"We will respect City until the end. At 2-0 you never know what can happen in football. It's been a good night of football but now in three weeks we'll have to fight very hard to be in the quarter-final."