Neil Lennon’s men took the lead in the 18th minute when Javier Mascherano deflected the ball into his own net, before Andres Iniesta scored an equaliser on the stroke of half-time.
Celtic dug deep in the second half, aided by a string of top saves from Forster, and looked set to hold Barcelona to a draw until Alba scored deep into injury time.
“Everyone is absolutely devastated – personally devastated and as a team too,” said Forster.
“We defended so well for 93 and a half minutes but then we have been punished from one cross at the end.
“Everyone is just gutted. You can make as many saves as you want but you need the result at the end of the game and we haven’t got that.”
Meanwhile, Iniesta felt Barcelona deserved to claim three points after dominating possession, and the Spain midfielder believes the Catalan side are now on the brink of reaching the last 16.
“Of course it leaves a great taste in the mouth when you win in the last second,” added Iniesta.
“It would have been unfair had we not won that game with the chances that we had. We were patient and in the end the goal arrived.
“The lesson we learned is that the team still have the confidence to turn a match around. We have achieved our objectives [in the group] up until now and the win leaves us in a good situation.
“This is football, however, and in terms of qualification, you can never take anything for granted.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news