Barça suffered only their second defeat of the season in Glasgow, the other being a 2-1 loss to Real Madrid in the second leg of the Spanish Super Cup in August.
However, they remain top of the group on nine points, two ahead of Celtic in second place. Benfica have four points and Spartak Moscow are bottom on three after the Portuguese side won 2-0 at home to the Russians on Wednesday.
“We are still in first place and we are relaxed,” said Lionel Messi, who scored in added time after earlier striking the frame of the goal. “I think we did everything well, we got into goal-scoring positions but the ball just didn’t go in.
“They were comfortable closing ranks in defence, waiting for a chance to counterattack, a corner or a free-kick and that’s how they managed to score the two goals.”
Barcelona’s coach Tito Vilanova and his players were generally gracious in defeat, and there was a sense they had even enjoyed the atmosphere in the ground despite the defeat.
“It’s a marvel, an example,” Xavi told reporters, while the club tweeted, “Congratulations to @celticfc for well-earned victory a day after their 125-year anniversary.”
Cesc Fábregas told Barcelona’s website, “There is no such thing as injustice or justice in football. You have to win and that’s it. We lacked depth, we had our chances and they scored the chances they had. We have to continue with our style of play, we’re very pleased with the season that we’re having. We have two games left and we’ll try to win them.”
Celtic’s victory ended Barcelona’s run of 17 away games in the Champions League group stage without losing. They were last beaten at Chelsea, 1-0 in October 2006, and had since won 11 and drawn six.