The Tannadice club lodged an appeal with the Hampden chiefs after the left-back was sent off in the 1-0 defeat to Derek Adams' team.
Douglas was dismissed by referee Kevin Clancy for a tackle on Ivan Sproule during the match in Dingwall that was deemed "serious foul play".
At an SFA fast track tribunal, it was ruled that Clancy had made the correct decision and the automatic two-match suspension would stand.
Douglas will now miss the Clydesdale Bank Premier League matches against St Johnstone and Inverness.
- Sports & Recreation
- Ivan Sproule
- Derek Adams
- Kevin Clancy