Many inside the game believe Diaz's departure has contributed to Liverpool's slide this season.
But Carragher said on The Overlap: “That’s where I think the hierarchy of the club has said Arne Slot is (only) the head coach. Arne Slot might’ve wanted to keep him.
“But they (the Liverpool hierarchy) said he’s 28, if we give him a new contract he’ll be on massive money.
“It was a good deal for Liverpool, and he’s going to look good in the Bundesliga because it’s not as good as the Premier League.
“Diaz was a very good player for Liverpool, but he wasn’t great – he wasn’t Firmino, he wasn’t Mane, he wasn’t Salah.
“He was a good player; Liverpool got some good years out of him and got a good price – it was a good deal for Liverpool.
“What they haven’t done is replace him, but if Wirtz becomes what we hope him to be, he’s a different player but he’s that player between the lines to the left, so you’ll get that from him.”