The Republic of Ireland forward, who will now serve a three-match ban, was given his marching orders by referee Andre Marriner following a high challenge on Alex Tettey soon after equalising from the penalty spot in the second half of the 1-1 Premier League draw at Carrow Road.
Stoke manager Mark Hughes described the decision as "harsh" and the club launched an appeal, but the FA believe Marriner was right to brandish a straight red.
A statement on the FA's official website said on Tuesday: "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."
The former Ipswich Town man will miss the top-flight clashes with West Ham, Aston Villa and Hull City,
Walters joins team-mate Charlie Adam on the sidelines after he was dismissed in the victory against Arsenal earlier this month.
