Danny Wilson is disappointed that United's appeals against the red cards shown to Michael Doyle and Ryan Flynn have been unsuccessful.
Captain Doyle received a red card just 15 minutes into Saturday's 1-1 draw at Scunthorpe United, whilst referee Steven Rushton also dismissed Flynn in the second half.
At a disciplinary hearing, held on Tuesday, both sending offs were upheld by the Football Association.
United boss Wilson told sufc.co.uk: "We thought we had a good case in attempting to get Saturday's decisions overturned so, obviously, we are very frustrated with today's decision."
The duo begin their three match suspensions at Saturday's game against Bury.