The Spanish midfielder said Barca were by far the better side and were worthy of securing a place in the tournament's final despite being ousted by the London club
The Catalan club have been denied access to the final following a 3-2 aggregate defeat against the Blues as a result of Tuesday's 2-2 draw at Camp Nou in the second leg of the semi-final tie.
Fabregas says that Barca deserved to go through but insists that the players will lift themselves up from this setback - the second in the space of a week after the 2-1 defeat to Real Madrid has left the team all but out of the race for the Liga title.
"Football is unjust sometimes," he told reporters after the game. "But if there is one way you want to lose, it is like this, being true to our style.
"I am 24 years old, and I have never seen Camp Nou react like this after a defeat. This is a great team, we will be back next year.
"Chelsea's playing style damaged us, we were far superior and we created several chances."
The Spain international then urged his players to switch their focus to what is left of the season, saying: "Now we have to think about the four Liga matches left and the Copa del Rey final."