The Jambos midfielder was sent off in the first half of the weekend's 3-1 loss to Dundee United for a tackle on Gary Mackay-Steven but the Edinburgh outfit were unable to pay the £1,000 to make a plea for their player.
"I spoke to John Fleming first thing on Monday morning," McGlynn said.
"He can't talk about a specific tackle, but he can talk you through what is serious foul play and we got the feeling we would not have stood an awful lot of chance with the appeal.
"We want to fight our corner, but have we £1000 to throw down the tubes at the minute?
"It's still quite a lot of money, and we felt that we probably would not win, so we didn't appeal."