The Canaries confirmed on their website that the Football Association had upheld referee Chris Foy's decision to dismiss Bunn after he was ruled to have handled outside his area in the 30th minute of the 1-1 draw at the Stadium of Light.
Bunn will serve his one-match suspension when Norwich face Wigan at the DW Stadium on March 30.
"An appeal by City against the red card shown to Mark Bunn by referee Chris Foy during Sunday's Barclays Premier League game away to Sunderland has been rejected by an independent regulatory commission appointed by the FA," the Norwich statement read.
"Mr Foy dismissed Bunn in the 30th minute of Sunday's 1-1 draw for denying a goal-scoring opportunity, when he charged down a back-header from team-mate Michael Turner outside the box under pressure from Sunderland striker Danny Graham.
"The relevant FIFA law states a player will be dismissed for 'denying the opposing team a goal or an obvious goal-scoring opportunity by deliberately handling the ball'.
"City appealed to the FA that Bunn had not deliberately handled the ball - but this was rejected and the keeper's suspension for the forthcoming Wigan game will remain in place."
With first-choice goalkeeper John Ruddy sidelined by injury, Bunn's suspension will mean a start for third-choice Lee Camp, who made his Canaries debut when coming on as a substitute at the weekend.