Miller was ordered off by Willie Collum for violent conduct after a tangle with United defender Darren Dods at Ibrox.
In a statement released by the Scottish Football Association, it was confirmed that Miller will be unavailable for two matches and that the appeal will not be heard by an independent review panel.
It read: "In accordance with the provisions for claims of wrongful dismissal, the referee, William Collum, was requested to review the circumstances of the player's sending off, in conjunction with the Referee Development Department.
"The referee has indicated that he is content with his decision, after confirmation of the player's violent conduct using both arm and leg.
"The claim is therefore dismissed automatically and will not be referred to the review panel. The player's automatic one-match suspension is applied, with 12 penalty points added to his disciplinary record."
The red card takes Miller over the points threshold and he will serve a two-match ban starting with the trip to Parkhead.