The Scotland international was punished for his stamp on Arsenal's Olivier Giroud during Saturday's 1-0 win at the Britannia Stadium.
Referee Mike Jones did not see the incident but it was picked up on television footage and although the Potters said they "vigorously appealed" the Football Association's decision to punish the player, an independent panel upheld the charge against the 28-year-old.
"Stoke City's Charlie Adam will serve a three-match suspension with immediate effect after an FA charge for violent conduct was found proven," said an FA statement.
"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 5 March 2014)."
Stoke chief executive Tony Scholes was unhappy the club's attempt to defend the player against the charge failed.
"I am extremely disappointed for the effect that this is going to have on Charlie and on the football club," he 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?"
The suspension means that Adam will be forced to sit out the forthcoming Barclays Premier League games against Norwich, West Ham and Aston Villa.