The Spanish giants dominated possession at Stamford Bridge, but it was Chelsea who looked most like scoring, with Willian hitting both posts in the first half before finally breaking the deadlock after the interval.
However, Lionel Messi ended his drought against Chelsea to register a crucial away goal, and Fabregas warned that it would be "suicide" to simply sit back and defend in the second leg at Camp Nou.
"It is such a shame really. I thought we were very good, we executed the game plan really well, we were compact, solid, played as a team and created lots of chances - Willian could have had a hat-trick - but we go home sad because a fantastic performance is not a fantastic result," he told BT Sport.
"It is still open though and we have showed that we can compete and we will need another excellent performance at the Nou Camp to go through.
"You have to have a lot of personality to play against this team who has 70% of the ball. We have to go there to attack and score because 90 minutes defending at the Nou Camp is an eternity, it is a suicide mission. We have to play our game."
Chelsea are now unbeaten in their last eight matches with Barcelona.