The Hoops skipper was ordered off by French referee, Stephane Lannoy, and now faces an automatic one-game suspension.
However, if the incident is deemed as violent conduct, Uefa have the option of increasing the ban to up to three matches. Three will rule him out of the back-to-back matches against Ajax and next month's visit to Parkhead of the AC Milan squad.
Neil Lennon believes that the initial foul on Neymar was worthy of a booking, but considers it was excessive to punish him with a red card.Further viewings of the incident will now take place before a decision is taken about an appeal.
Lennon said: "We are looking at appealing the red card. I think we should. It was soft."
Although he is disappointed that his skipper did not manage to avoid such a flashpoint, Lennon believes Neymar's tendency to make the most of any contact was a significant factor in the ref's decision.
Mikael Lustig was booked for a foul on the Brazilian in the first half and Lennon said of the Brown challenge: "I didn't think the initial tackle was a severe one. It's a physical game.
"I don't think Neymar does himself any favours by the way he behaves at times. Our supporters are very respectful of great players.
"Iniesta walked off to a standing ovation from the Celtic support. Neymar, after the incident, got booed every time he touched the ball.
"I don't think I need to justify my defending of my captain. The sending-off was uncalled for."
Lennon was delighted at the way his side played before and after the pivotal moment.
"I don't remember being under immense pressure," he reflected.
"Obviously, they had a lot of the ball. But my keeper had nothing to do for a long stretch of the game. Up until the sending off, we were comfortable. It got stretched late on when we went for it, but Fraser made some excellent saves to keep it at 1-0."
However, the defeats in the San Siro on Match day One and again last night, when at least a point was within touching distance each time, have left Celtic bottom of Group H without a single point.
Lennon did take some consolation from the fact Ajax drew 1-1 with AC Milan, but knows there is no more room for slips.
He said: "The result went for us in Amsterdam. We have to try and take four points from our next two games then beat Milan here as well if we are going to have aspirations about qualifying."