Despite an appeal from the Parkhead club, McDonald stood by his decision after looking at the incident again on video.
Tony Mowbray says he is "bewildered" by the Scottish Football Association's appeals procedure, which allows the referee to act as judge and jury.
Brown, who scored the winner for Scotland in the 1-0 friendly win over the Czech Republic at Hampden on Wednesday, will now miss Sunday's trip to Falkirk in the SPL.
He has also incurred a two-match fixed suspension from March 14 for reaching the disciplinary threshold of 18 points, and it still rankles.
"Yesterday's decision is really disappointing," Brown told the club's official website. "We challenged the original red card because we thought it was wrong, and I still think that is the case.
"I know our view was shared by many other people and players that I've spoken to with the Scotland squad this week.
"Now that the referee has had a chance to see the video footage of the whole incident, I can't understand why he still feels that I deserved a red card.
"What happened in the incident is clear for everyone to see and decide for themselves.
"I've been lucky to come through recent injury problems and get back in the team, to have a three-match suspension in the same week as scoring for my country is a real blow.
"I'll just have to deal with missing three games, however harsh I might think that is."
Meanwhile, Saturday's Under-19 match between Celtic and Rangers at the Excelsior stadium in Airdrie is off due to bad weather.
The game will be played behind closed doors at Celtic's Barrowfield training ground.
Source: Team Talk
Source: Team Talk