Cardiff City took the matter to the FAW who rejected the appeal.
As a result Purse missed the defeat at Q.P.R. and also misses Saturday's game at home to Southampton. It means that Purse will have missed three of the 6 games in December through suspension.
Dave Jones was not happy with the decision of the FAW.
"Whoever made the decision at the FAW needs to take a long look at themselves because I can't believe that they've ever played the game," said Jones.
"We asked the FAW to look at it and they decided it was a red card offence.
"The sending off was absolutely ridiculous, I've been in the game a long time and that was not a red card offence.
"I've been told that the club has appealed five times to the FAW over recent years and that they've never had any decision turned over yet."