Brown, who is guaranteed to miss the next Champions League group game at home to Ajax, could face a further suspension if a disciplinary panel sees fit.
Celtic were unable to appeal against the red card and the subsequent one-game suspension, but would be able to contest any additional ban.
The Hoops captain's fate will be decided by the Uefa group after he was red carded by referee Stephane Lannoy for aiming a kick at Barcelona's Neymar during Tuesday's Group H clash.
Parkhead manager Neil Lennon has said that while the club wouldn't contest the current one-game ban, the SPL Champions would argue any decision to rule him out of further Champions League games.
UEFA's Control and Disciplinary Body meet to review every red card in the competition and it is not a foregone conclusion that Brown will be hit with a further sanction.