The Hoops were helpless to prevent Catalan cracks Barca from recording a narrow 1-0 victory at Parkhead.
The agonising defeat leaves Neil Lennon's side, who lost 2-0 to AC Milan in the San Siro last month, languishing in bottom spot in Group H.
But the Swedish full-back is refusing to accept that Celtic's chances of progressing beyond the group stage again this season are over.
He believes the Scottish champions can still finish in second spot in their section and is not thinking about third place and the consolation of a Europa League spot.
Lustig said: "We need to believe in ourselves and have faith. We have got Ajax at home next and I think we have to pick up all three points.
"Milan have to face Barcelona now. If Barcelona take six points against Milan and we can take some points off Ajax then we have Milan at home. There is all to play for."
Celtic contained opponents who were clearly missing Argentinian talisman Lionel Messi up front, with the tie level at the break.
But the game turned with the controversial red carding of Hoops captain Scott Brown for an off-the-ball challenge on Brazilian superstar Neymar.
French referee Stephane Lannoy had no hesitation ordering the Scotland internationalist off for the second-half challenge on the forward.
Lustig, though, felt his skipper only deserved a caution and should have been allowed to see out the 90 minutes.
He commented: "I thought it was maybe a yellow card. I thought a red card was a little bit harsh.
"We are, of course, disappointed. We wanted some points, we needed some points. Before they scored the first goal, they didn't create any chances. We were in the game.
"Scott has said that he is sorry of course, but, like I said, I still think it was a little bit harsh.
"His leg was maybe touching him, but he didn't think it was a red card."
Lustig was impressed with how Celtic performed after Brown received his marching orders and felt they could have levelled the match.
James Forrest forced a fine save from Barcelona keeper Victor Valdes and Charlie Mulgrew should possibly have netted with a chance after that.
Lustig recalled: "After Scott was sent off we had our two best chances. The game didn't change that much.
"But, of course, it is hard to play against Barcelona with 10 men. It was too bad."
However, the defender confessed that Celtic, who beat Barcelona to reach the last 16 last season, had needed Fraser Forster to keep them in the game during the latter stages of the match.
The Englishman boosted his chances of being part of his national squad in the build-up to the World Cup next summer with a sensational double save at the death.
Forster denied Neymar and then substitute Alexis Sanchez in rapid succession. He also pulled off another fine block from Neymar after that as the Brazilian ran clear through on goal before being thwarted by the shotstopper.
Lustig recalled: "It is too bad that they didn't mean something for us.
"But we know Fraser is a world-class keeper."