Walters was dismissed in the 78th minute of the Premier League contest at Carrow Road for a foul on Canaries midfielder Alexander Tettey.
The Republic of Ireland forward will now serve a three-match suspension and the Potters have reacted angrily to the decision, which they claim shows inconsistency.
The news is a major blow to the club who are facing three rivals in the scrap to avoid relegation in West Ham, Aston Villa and Hull City, whilst Walters is suspended.
A statement on the FA's official website read: "Following an Independent Regulatory Commission hearing today, a claim of wrongful dismissal concerning Stoke City's Jonathan Walters was rejected.
"Walters was dismissed for serious foul play during the game against Norwich City on 8 March 2014.
"His three-match suspension will commence with immediate effect."
Following the FA's announcement about Walters, Stoke issued their own statement which said: "The club gave careful consideration to whether or not to appeal Jon's sending-off but we felt compelled to do so in the interest of consistency after three incidents of a more serious nature in the Premier League last weekend failed to result in red cards.
"We are disappointed with the lack of consistency that this decision seemingly supports."
Walters' red card came five minutes after he had scored Stoke's equaliser from the penalty spot.
After the match Stoke boss Mark Hughes criticised Andre Marriner's decision to show the red card.
"I've looked at the incident and there is contact and Jon has accepted that he caught him," Hughes said.
"But both players had their feet high and I think the punishment was too harsh for the crime. Both players just intended to win the ball and Jon just caught him with his follow through."