Komphela was seemingly frustrated with referee Phillip Tinyane and his assistants after Saturday's Soweto Derby, which ended 1-1.
The Amakhosi mentor argued that 'no one should be above the game' in his assessment of the way the officials handled proceedings, and called for international officials in future.
Tinkler, however, refused to back his counterpart and chose not to entertain the topic of referees, despite his side having harshly been denied a penalty late on.
"I don't really want to comment on the referee, to be honest," said a submissive Tinkler.
"I'd rather leave that to the people in charge, which are the match commissioners. They will write their reports and they will assess the referees."
The draw leaves Bucs 13th in the Absa Premiership standings, with 17 points from 15 games. They take on Ajax Cape Town in their next League fixture on Wednesday.