No excuses from Fabregas
The visitors dominated proceedings for large parts of the match at Celtic Park, but were unable to convert their chances.
"There is no such thing as injustice or justice in football. You have to win and that's it," Fabregas said.
"We lacked depth. We had our chances, but failed to convert them, whereas they scored with the few chances they had."
Fabregas then went on to voice his satisfaction with Barcelona's performances so far this term, and stressed that they will do their utmost to win their remaining two group games.
"However, we are very pleased with the season that we are having so far, and we have to stick to our style of play and our own philosophy," the Spain international said.
"We have two games left in the group stage and we will try to win them."
Barcelona resume La Liga action away against Mallorca on Sunday.