The 23-year-old's misplaced backheel in stoppage time at the end of the first half led to Barcelona's opening goal and Fabregas failed to lift his game in the second as the Spanish champions dominated to win 4-3 on aggregate .
"Great support from the Arsenal fans. I take full blame for the result tonight," Fabregas wrote on his Twitter page. "One of the worst moments of my life. I apologise."
Fabregas struggled on his return to the side following a hamstring injury as Barcelona's midfield trio of Xavi, Andres Iniesta and Javier Mascherano controlled the match with their intricate passing, leaving Arsenal chasing shadows.
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Arsenal equalised when Sergio Busquets deflected a corner into his own net in the 53rd minute but the dismissal of striker Robin van Persie three minutes later resulted in wave after wave of Barca attacks with Lionel Messi and Xavi making the game safe.
Fabregas's team-mate Jack Wilshere also used the social network site to thank the Arsenal fans and congratulate Barcelona on victory.
"Arsenal fans great as always! Sorry about the result, good luck to Barca, great team! Oh yeah and the ref was good as well...," the English teenager wrote on his Twitter page.
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