Sturridge, 27, missed a number of goalscoring chances as Liverpool lost 1-0 at Anfield to Southampton, leading to their exit from the EFL Cup at the semifinal stage 2-0 on aggregate.
Carragher is concerned that Sturridge’s pace has been hampered by a string of injuries since his move from Chelsea to the Reds in 2013.
“Sturridge is a completely different player now to when he first came to Liverpool,” Carragher told Sky Sports. “You could link him with Sadio Mane when he first came because the whole point of Liverpool buying Sturridge under Brendan Rodgers when I was at the club was that he gave us penetration in behind, he had pace.
“But there was one occasion in the game [last night] where he fell over into the hoardings in front of The Kop and I thought he had to get that ball. I don’t know if his pace has completely gone or whether he’s that worried with injuries that he pulls out of something.
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“Sturridge is not the player to run in behind, so you can forget about him replacing Mane. All he does is come to feet now. The only reason to have Sturridge in the team is for his finishing ability. You’ve basically got to put things on a plate for him. Liverpool did that against Southampton and he didn’t finish.
“More often than not you cannot question his finishing, but he doesn’t do anything else in a game now, whereas he did when he first came. He’s had a really poor night in front of goal.
“That’s the case with that type of striker now; if they’re not a target man or don’t run in behind, everything has got to be put on a plate. So when he doesn’t score you’re basically down to 10 men because they are not offering anything else whatsoever.
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“You have to criticise Sturridge because he missed chances, but when you look at his Liverpool record – his finishing and goal-to-game ratio – it’s fantastic. But I’m talking about his pace and his overall game because when he doesn’t score it’s like playing with 10 men.”
Liverpool have won just once in 2017, with the side struggling since Sadio Mane departed for the Africa Nations Cup to represent Senegal.