The midfielder was sent packing by referee Stephane Lannoy for aiming a kick at Brazilian ace Neymar after he had brought the Nou Camp star down.
Celtic boss Neil Lennon had told SportTimes the club intend to appeal the decision, but Brown has apologised for his moment of madness.
He said: "I realise that I made a mistake in getting sent off. It's something that happened in the heat of the moment but I shouldn't have acted in this way.
"I still think it was a harsh decision. However, I recognise that I made a mistake and put myself and my team-mates in a difficult position.
"I need to live with that and there is no-one more disappointed than me about losing the match.
"There wasn't a huge amount of contact at all, to be honest, but I have to accept responsibility for my actions - and I do."
Brown also told the official Celtic website: "The team deserved to get something out of the game after playing so brilliantly and putting in so much effort against one of the best sides in the world.
"I was also disappointed for the supporters after the incredible backing they gave us during the game. They were magnificent once again. It was another fantastic performance from the lads."