Levein claimed the referee "bottled" several major decisions during his side's 3-1 Clydesdale Bank Premier League defeat by Rangers in May.
The United boss was found guilty of "bringing the game into disrepute" and "criticising the performance of match officials in such a way as to indicate bias or incompetence".
But the former Scotland defender had no regrets and an appeal is being considered.
"I said what I honestly felt at the time. It was a poor performance and I'm still angry about it," Levein said.
"I wasn't going to go in and apologise for anything I said."