Barca suffered only the second defeat of the season in Glasgow, the other a 2-1 loss to arch-rivals 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. 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," Barca's World Player of the Year Lionel Messi, who netted in added time and earlier struck the frame of the goal, told reporters.
"I think we did everything well, we got into goal-scoring positions but the ball just didn't go in," added the Argentine, who became a father for the first time when his son Thiago was born on Friday.
"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."
"It's a marvel, an example," Xavi told reporters.
Celtic's victory ended Barca's run of 17 away games in the Champions League group stage without losing.
