Mikel Arteta’s side left Elland Road with a point after they were reduced to 10 men for the final forty minutes in Yorkshire after Pepe was given a red card for headbutting Ezgyjan Alioski.
‘I’m not saying that it’s a proper full-on headbutt but you can’t do that to people in this day and age,’ Wright told Premier League Productions.
‘You can’t get into people’s face like that. Alioski has gone down like he’s really got a proper headbutt but at the same time that’s just totally unprofessional and just poor from him.
‘From somebody that has been complaining about not getting enough game time, somebody that has now got his chance and he’s let everybody down.
‘He has let everybody down and i’m very disappointed in him simply because I don’t know who his team is around him but he’s come to the club, we’ve spent a lot of money on him.
‘He’s someone that we have a lot of faith in and he seems to me that he’s not getting better, he’s actually getting more in himself and more frustrated, where you want to see him improving. He needs better advice around him.’
The Gunners actually improved in the main after Pepe’s dismissal and Bukayo Saka had a glorious chance to snatch all three points but he failed to convert after being put through on goal.
Pepe will miss games against Spurs, Wolves and Burnley following his red card.