Brown was shown a straight red following a kick on Brazilian Neymar, but the player has stated that he felt his dismissal was harsh.
"I realise that I made a mistake in getting sent off last night. It's something that happened in the heat of the moment but I shouldn't have acted in this way," Brown told Celtic's official club website.
"I still think it was a harsh decision. However, I recognise that I made a mistake and put myself and my teammates 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."