The SFA rejected Celtic's appeal after referee Dougie McDonald reviewed the incident and declared himself "content with his decision".
However, Mowbray cast doubt on the effectiveness of the appeal process in Scotland and re-stated his belief that Brown should not have received his marching orders.
"My own personal view is that it wasn't a sending off," he said. "I think we had grounds to appeal the decision.
"I'm not sure what an appeal is in the true sense of the word. If the referee who made the decision on the day looks at it and decides he got it right and that's the end of the matter then it seems a strange appeal system.
"I was unaware of how the appeal system works in Scotland and yet if the guy making the decision looks at it and decides he was right then that's the end of it and we have nowhere else to go.
"It seems strange that we can't go to somebody else to have a look at it, not from the referee's angle.
"In the last two Old Firm games, there have been some pretty big decisions, to the point where we had an official come out and apologise for a wrong decision.
"I think that should be applauded and probably was applauded at the time."
Mowbray said there was also controversy over Marc-Antoine Fortune's effort that was chalked off in the 1-1 draw with Rangers at Celtic Park earlier in the season.
"I couldn't really see a free-kick or a foul there and then another Old Firm game comes along and another contentious decision which had a big effect on the result and the game - almost politically it couldn't go against you.
"If it had been upheld, it would've been proven as a wrong decision. In my mind, the referee owned up to a wrong decision on the first game.
"In the second game, the general consensus thought it was a goal. I don't want to get dragged too much into it, but you can see my point."
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