Fabregas apologised for the mistake which helped Barca make the breakthrough.
Fabregas, returning to his boyhood club for the first time, inexplicably tried to backheel the ball to Jack Wilshere on the edge the Arsenal penalty area, but gave it straight to Andres Iniesta - who set up Lionel Messi.
On his Twitter account, the Spaniard said: "Great support from the Arsenal fans.
"I take full blame for the result tonight. One of the worst moments of my life. I apologise."