Robbie Neilson has been given a two-match suspended ban for comments about referee Willie Collum after Hearts' game against Hamilton on 29 August.
The Tynecastle head coach will only serve the suspension if he breaches league rule 72 again before the end of the current season.
Neilson commented after the match that Collum had been wrong to send off Hearts defender Callum Paterson.
And he said the squad had trained with 10 men to prepare for a red card.
The Scottish Football Association's compliance officer issued a notice of complaint for a breach of disciplinary rule 72, stating of Neilson that "in an interview with the BBC you criticised the performance of the Match Officials in such a way as to indicate bias or incompetence on their part".
Hearts' appeal against the notice was rejected when the disciplinary tribunal met on Thursday.
Neilson remarked after the match at New Douglas Park: "We actually practised going down to 10 men because of the environment we're coming to and the officials who are taking the game and we have to do that.
"In the recent past, the statistics involving the officials have shown a lot of red cards against us, so we have to prepare for it.
"The next time we get these officials, we will again train with 10 men."
Patterson's red card was rescinded a few days later.