The Dees conceded in the 11th minute when Brian McLean scored for the Arabs but the ball appeared to go out of play in the lead-up and Brown felt that linesman Andrew McWilliam completely missed the call.
"An official has cost this club a quarter-final replay and the chance to get to a semi-final," he said.
"I'm pretty bitter about a decision that didn't go our way.
"It was a clear throw-in, but it wasn't given and ultimately resulted in the free-kick leading to the goal.
"I don't need to talk about how to defend it because it shouldn't have happened.
"I spoke to the referee's supervisor Bob Valentine and he said the ball was out.
"It's human error, but it's a sore one to take. I was 10 yards away, it was right there and how he can't see it...
"That one decision, you need them to be on their game. They don't do it right and it's cost us the game.
"Take that away, it's an even game and I think we would have got a replay. That's the bitter pill that's left in the mouth."