Former Gunners midfielder Arteta signed a three-and-a-half year deal with Arsenal shortly before Christmas to become Unai Emery’s permanent replacement at the Emirates.
In his first two matches in charge, Arsenal drew at struggling Bournemouth and surrendered a lead to be beaten by Frank Lampard’s Chelsea.
Pierre-Emerick Aubameyang gave Arsenal an early lead over Chelsea on Sunday but goals from Jorginho and Tammy Abraham saw the visitors fight back to earn the three points.
Wright says Mustafi was ‘absolutely petrified’ of Chelsea’s Abraham during the Premier League match and has urged Arteta to offload the Arsenal defender.
‘Mustafi was absolutely petrified of him [Abraham],’ Wright said on Match of the Day 2.
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‘You have got someone like Arteta coming in but there’s nothing you can do to coach a defender of his experience now, those are the type of players he’s got to be looking to get rid of.’
Despite criticising Mustafi, former Arsenal and England striker Wright insisted there were positives to take from Arteta’s first home match in charge of the Gunners.
He added: ‘When you look at the two games there’s definite improvement in Arsenal.
‘You just think what they could have done had they gone with the appointment after the Leicester game at the international break.
‘It’s one and two touch all the way and its really quick. Fantastic zip, the fans should be happy with what they’re seeing at the moment but give Chelsea credit for what they’ve done today.’
Arsenal, currently 12th in the Premier League, face Manchester United on New Year’s Day.