Emre Can scored the Reds' first with a delicate chip down the centre of the goal but that is where the fortune ended for Jurgen Klopp's side, with Willy Caballero producing fine saves to keep out Lucas Leiva, Philippe Coutinho and Adam Lallana.
Manager Jurgen Klopp confirmed after the game that James Milner was set to take the fifth and final regulation spot-kick for the eight-time tournament winners, leaving their main central attacker out of the list of participants.
Former defender Carrager, who lifted the three-handled trophy on three occasions during his playing career, questioned the reasoning behind the decision to leave out Sturridge from the game-deciding shootout.
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"He’s one of the few real technical players Liverpool have got out there. Sometimes it won’t go to the fifth penalty and you want your best players to take them.
"You think there’d be more chance of Daniel Sturridge scoring than Lucas Leiva. The fact that the shootout has gone on and Daniel Sturridge hasn’t taken one for Liverpool is just stupid."