Brown appeared to be the victim of an off-the-ball incident during the 1-1 draw at Celtic Park on Wednesday night.
Ronaldo escaped punishment even though the Belgian assistant referee was just a few yards away and Brown has suggested the Manchester United star received special treatment.
Brown told the Daily Record: "Maybe it's because it's the Champions League. Maybe it's because it's Manchester United.
"Or maybe it's just because it's Ronaldo we're talking about but I don't think there are many situations in football where a referee would let someone away with something like that.
"Maybe the ref didn't see it too well but his linesman was only a few yards away and must have had a clear view.
"I just don't think there should be one rule for the rest of us and another one for Cristiano Ronaldo."
Brown added: "At the very least he should have been booked and been given a talking too. That's what I would have expected if it had been me."