Celtic appealed but after McDonald looked at the incident again on video on Thursday, it was rejected.
A statement issued on the club's official website read: "We are amazed at this decision and believe it is the wrong one."
And speaking before Sunday's trip to Falkirk, manager Mowbray said: "Having watched it back, my own personal view is that it wasn't a sending off.
"But was it an appeal? We didn't appear to get an appeal in the true sense of the word.
"The referee who made the decision on the day looks at it and decides if he gets it right, that's the end of the matter.
"I was unaware of the appeals decision in Scotland and it seems a strange appeals system.
"It seems strange that we can't go to someone else and look at it and make a decision, not from a referee's angle, not from the club's angle but just an unbiased look.
"It seems a strange decision but we have to abide by it."
Source: Team Talk
Source: Team Talk