The Scotland international was found guilty of violent conduct after his stamp on Arsenal's Olivier Giroud during Saturday's 1-0 win at the Britannia Stadium was missed by referee Mike Jones but picked up by television footage.
Stoke contested the FA's decision to charge the player but an independent panel upheld the charge against the 28-year-old.
"I am extremely disappointed for the effect that this is going to have on Charlie and on the football club," Scholes told stokecityfc.com.
"However, I am not surprised because clubs like ours very rarely succeed in appeals to the FA.
"We put together a strong defence which was based upon the facts, which were that Charlie needed to plant his foot, and in changing direction his eyes followed the ball at all times.
"How can anybody other than Charlie say what intent was there? How can the FA possibly justify this decision in the light of recent incidents which were far worse at other clubs, which have gone unpunished?"
Last month Manchester City's Yaya Toure escaped punished after appearing to aim a kick at Norwich's Ricky van Wolfswinkel, leading Chelsea manager Jose Mourinho to state: "The message is clear: the players can do what they want if the referee doesn't see".
Adam will now miss league matches against Norwich, West Ham and Aston Villa.
A statement from the FA confirmed the midfielder's punishment.
"Stoke City's Charlie Adam will serve a three-match suspension with immediate effect after an FA charge for violent conduct was found proven," it said.
"The incident with Arsenal's Olivier Giroud, which was not seen by the match officials but caught on video, occurred during the fixture between the two sides at the Britannia Stadium on Saturday 1 March 2014.
"Adam had denied the charge, but it was found proven at an Independent Regulatory Commission hearing today (Wednesday March 5 2014)."
- Sports & Recreation
- Olivier Giroud
- Charlie Adam