Cesc Fabregas grabbed the winner with 15 minutes left at Parkhead to confirm a second straight defeat for Neil Lennon's men after they returned home from the San Siro with a 2-0 loss to AC Milan in their opening game.
Celtic must now seek to make up lost ground when they take on Ajax over two games on October 22 and November 6.
The Hoops then close out their campaign with the return against Milan in Glasgow on November 26 and a trip to Barca's Nou Camp on December 11.
But Commons believes Celtic need to win three of the four matches if they are to match last season's feat of reaching the knock-out stages.
He said: "I think we need to win our two home games and then we need to go on the road and try to pick up a win and that's going to be a mammoth task looking at the games we have left."
Celtic will have to do without Brown for the first meeting with Ajax after he was handed an automatic one-match ban.
But he may miss the second game in Amsterdam and even the match against Milan after UEFA confirmed their Control and Disciplinary Committee would look at the midfielder's dismissal to consider whether a longer suspension was necessary.
Lennon's men had looked comfortable against the Spanish champions until Brown's moment of madness swung the tide in their opponents' favour.
The Celtic boss argued Neymar made the most of the incident with Brown by rolling about but Commons told Sky Sports News that the Celtic players had to adopt a physical approach with the B£49million signing from Santos.
"He got some rough treatment," Commons said. "He's an outstanding player and you need to get tight to him and you need to rough him up."
The former Scotland international added: "It's a similar sort of feeling as after AC Milan.
"We feel as if we've put in a lot of hard work, but ended up getting an unlucky decision from the referee and your back is against the wall from then and you've got 20 minutes to try to stop the best team in the world from scoring.
"You're practically up against the impossible when you have 11 men, not only to get the ball but to create chances. For 60 or so minutes we defended magnificently and kept them at bay. I can't think of Fraser Forster having to make a save in the first hour.
"But then Scott gets sent off and obviously our game plan has to change - a little bit of lady luck would have been nice."
Celtic had stunned Europe last year by beating the four-time European champions at Celtic Park but even though Barca were without the injured Lionel Messi this time, a repeat of that famous result was always unlikely.
Now defender Efe Ambrose says the team must focus on their Dutch double-header.
"The difference in the match last season is that we scored first and it eased the pressure, but this time there was a red card and we missed our chances, but the teamwork and concentration was very good," he said.
"The most important thing is to look forward and the games with Ajax, we need to concentrate and see what we can do at home and then away, I believe we still have a chance to go through the group.
"Everything in football is difficult but we just need to wait and see what happens with Ajax and also what happens with Barcelona and AC Milan and then we will see what our chances of going through are like."
Full-back Mikael Lustig added: "Of course we are disappointed, we want some points, we need some points. Before they scored the goal they didn't create much and we were in the game. We created our two best chances with 10 men but couldn't take them.
"We have Ajax at home next and we really need three points."
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