Cavanagh, shown a straight red card for his high challenge on midfielder Robbie Weir, will start a three-game ban and misses Saturday's home game against Chesterfield plus successive away fixtures at Plymouth and Oxford.
Dale's chief executive Colin Garlick said: "I'm really disappointed because looking at the laws of the game and the FIFA interpretation and guidance to referees, I believe that Peter's actions were reckless with respect to him not having regard for his opponent, which should warrant a yellow card.
"There was no malice or intent in his actions and I believe the red card should have been reduced. I'm disappointed that the FA haven't come to that conclusion based on what we submitted."
- Sports & Recreation