Carragher believes Robertson's game doesn't suit manager Arne Slot's system.
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After Sunday's draw with Manchester United, Carragher said on Sky Sports: "This manager's style is slightly different to Klopp's. It's not as gung-ho. Liverpool have a lot more goals in the team than Arsenal have.
"Liverpool still concede goals. Liverpool need to sign a full-back in January. I think at left-back.
"Robertson is an absolute legend, he's just hanging on in every game now."