Anelka played for Liverpool on a six-month loan from Paris St Germain under previous manager Gerard Houllier, but the Reds decided not to buy the striker for £12million.
The Reds instead used the cash to sign El-Hadji Diouf.
Carragher said: “I think it’s a bit strong to say it was one of the worst decisions ever, but it’s fair to say it was a mistake.
“You look at Anelka now – he was top scorer in the Premier League last season. It’s in the past now, but it was probably something that never went our way.”
