Georgios Samaras' header from a Charlie Mulgrew free-kick in the 18th minute went in off the back of Barca's makeshift centre-back Javier Mascherano to give the visitors a shock lead, but a minute before the break midfielder Andres Iniesta levelled for the hosts.
Then, with the four minutes of added time almost played at the end of an exhausting evening in which Celtic goalkeeper Fraser Forster had been outstanding, Alba broke Hoops' hearts when he sneaked in at the back post to knock an Adriano cross home from close range to secure a 2-1 win for Tito Vilanova's side.
The Scottish champions remain second behind Barca in Group G with four points from three matches ahead of the return game against the Catalan giants in a fortnight, before facing Benfica away and Spartak Moscow at Parkhead.
Lennon, who is hoping to have Samaras back fit for the Barcelona rematch after the Greece striker left the action with a twisted ankle just before the equaliser, said: "Of course we have the belief. They have performed well in the three games so far. There are three games to go and anything can happen.
"Barcelona were always heavy favourites (to win the group) and we felt it was a three-way fight for second place.
"We have to pick them up and go again, but I don't think they will need much picking up. They can take a lot of satisfaction from that game against Barcelona."
Lennon said the anger he felt as he sat in the post-match press conference was all to do with the "circumstances" of their defeat.
He said: "We just had to see out one more attack, but unfortunately it didn't go for us.
"On balance, Barcelona deserved to win the game - I understand that.
"But looking at the two teams beforehand people would have said it was a walkover and it was far from that."