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The veteran centre-back was dismissed shortly before the break at Molineux with the VAR upholding the decision of referee Craig Pawson, who judged David Luiz had made contact with the heel of Willian Jose.
Ruben Neves converted the resulting spot-kick to cancel out Nicolas Pepe's opener and Joao Moutinho scored the winner in a match the Gunners finished with nine men after goalkeeper Bernd Leno also saw red.
Head coach Mikel Arteta confirmed Arsenal had launched an appeal against the decision but the Football Association (FA) has dismissed the claim, meaning David Luiz will miss out against Aston Villa on Saturday.
An Arsenal statement read: "The Football Association have confirmed to us that the red card given to David Luiz on Tuesday against Wolverhampton Wanderers will stand.
"We have worked really hard to overturn David Luiz's red card. We presented our case to the FA but are disappointed that our appeal has been unsuccessful.
"We accept the FA's decision and continue our preparations for Saturday's match against Aston Villa."
Southampton enjoyed a slither of good news from their 9-0 embarrassment at Manchester United, though, after the FA did overturn a red card awarded to Jan Bednarek.
The defender was harshly dismissed by referee Mike Dean for a last-man foul on Anthony Martial with the score already at 6-0.
Following the game, Saints dismissed reports they had officially requested Dean and fourth official Lee Mason no longer be involved in their matches.
Bednarek, though, is free to feature when Southampton aim to rebound at Newcastle United this weekend.
A club statement read: "Southampton defender Jan Bednarek will be available for Saturday's trip to Newcastle, after the club successfully appealed his dismissal in Tuesday's match against Manchester United.
"Bednarek was shown a straight red card during the second half at Old Trafford, having been judged to have denied Anthony Martial an obvious goalscoring opportunity.
"The club immediately appealed the decision, and a review by an independent regulatory commission at the Football Association has now led to the card being rescinded."