The Dens Park boss challenged a one-match ban offered earlier this month after he was charged with "making comments in a media interview that criticise a decision and the performance of the match officials in such a way as to indicate incompetence."
Brown was unhappy with decisions made by referee Alan Muir during a 1-1 draw with Aberdeen, which confirmed his side's relegation from the Clydesdale Bank Premier League. An SFA disciplinary tribunal convened on Thursday to consider the case and found Brown to be in breach of the rule and issued a censure.
Brown was unhappy with a penalty award which earned the Dons a point after claiming midfielder Peter Pawlett dived to win the spot-kick.
Speaking after the game, the Dees boss said: "You expect officials to do their job and it makes a mockery of it.
"(We have) a referee that can go to his work on a Monday morning and can sleep well tonight.
"This is our livelihoods. It has been taken out of our hands. It is a shocking decision for the penalty kick.
"That has taken us down. That decision has taken us down and it's a disgrace.
"It is the worst thing I have ever seen. He can't get it right."
Brown initially threatened to quit football if punished for the comments before later retracting the claim, which he described as "heat of the moment."