The German has made five appearances in the League Cup and Europa League this season but he is yet to start a league game and has fallen down the pecking order since the arrival of David Luiz from Chelsea on transfer deadline day.
Mustafi was given a starting-berth at Anfield by head coach Unai Emery, but the former Valencia defender could not make the most of that opportunity and was shaky from kick-off.
The 27-year-old opened the scoring for the Reds by turning a low cross into his own net in the seventh-minute.
According to pundit Carragher, 'Mustafi's days in the Premier League are gone’ and the North Londoners must ship him out as soon as possible.
‘I think those days are gone, Mustafi playing in the Premier League,’ Carragher told Sky Sports after Arsenal’s defeat to Liverpool from the Carabao Cup.
‘I don’t think how well he played her tonight would change that. He’s just one of those defenders who make mistakes and it affects other people.’
‘When you play with someone like that it makes you nervous. Your goalkeeper, your full-backs… you can’t play your own game because you’re always worried he’s going to make a mistake and are half-covering him.’
‘I think probably for Arsenal the quicker he’s gone the better for everyone.’
Mustafi joined the Gunners from Valencia in August 2016 for an undisclosed fee, reported to be in excess of £35 million and he has since featured in 84 Premier League matches for Arsenal.