The Catalans came into last night's semi-final second leg on the back of successive defeats, losing 1-0 to Chelsea in the reverse fixture at Stamford Bridge and then suffering a home defeat to arch rivals Real Madrid.
Barcelona's losing run stretched to three games at the Nou Camp as the Blues somehow overcame John Terry's first-half sending off to secure a 2-2 draw and progress to the Munich finale.
Fabregas was disappointed not to defeat the west Londoners given Barca's dominance but insists they will overcome the disappointment.
"It's a painful way to go out because we were superior," he told the club's official website, www.fcbarcelona.com.
"The result in Stamford Bridge is what did us in.
"We played a great game, we dominated and we created a lot of chances. We didn't sacrifice our style.
"It's painful to be eliminated this way, seeing that we had a lot of chances to score.
"It's a very hard blow. We have to hold our heads high. [Next year] we'll have the chance to do important things."
Fabregas' sentiments were echoed by a number of his Barca team-mates on Twitter.
Isaac Cuenca, who set-up Sergio Busquets for the hosts' opening goal, said: "We fought until the end. Fans, I'm very sorry. We'll pick ourselves up with your help #forcabarca."
Andres Iniesta doubled Barcelona's advantage as half-time approached and posted after the match: "It's a difficult and hard moment. We did everything to be in the Munich final, but it wasn't meant to be..."
Dani Alves was another to express his disappointment via the social network, adding: "I'd like to thank all the Cules for your support and, at the same time, apologise for what happened. We tried but it wasn't meant to be."