The Gunners fell to a 3-1 Premier League defeat at the Etihad on Sunday and the Germany international struggled as City targeted the right side of the visitors’ defence, with Sergio Aguero netting a hat-trick.
Mustafi joined Arsenal from Valencia for around £35 million in the summer of 2016, but Carragher has been left unimpressed by the 26-year-old.
“Mustafi has never been good enough since the day he walked in the door,” said the Sky Sports pundit.
“That’s the reason why all the goals come down there.
"To see Arsenal defend like that, there’s a big job there for Unai Emery to do.”
Former England right-back Alex Scott pointed the finger at Stephan Lichsteiner, the veteran Swiss defender who joined Arsenal from Juventus last summer.
"He's all over the place,” she said. “He doesn't know when to go and close down his player," she added.
"He's leaving... a bit half-arsed and that's why between him and (Alex) Iwobi, they're getting popped around down this side.”
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