The Reds surrendered a 2-0 lead at Dean Court twice as Bournemouth took advantage of the visitors' leaky defence with three goals in the final 15 minutes.
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Jurgen Klopp has used James Milner and Lucas Leiva in defence this season
The defeat saw Liverpool fall behind in the title race and drop to third in the Premier League table - four points off leaders Chelsea.
Redknapp was not surprised to see his former club concede four goals at Bournemouth and has urged Klopp to invest in a new centre-half and left-back in the January window.
Redknapp told the Daily Mail: "Liverpool are not going to win the title this season unless they sort out their defence.
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Jurgen Klopp saw Liverpool surrender a 2-0 lead twice against Bournemouth
"They sorely missed the injured Joel Matip and with two midfielders — Lucas and Milner — in their back four I was not surprised that they conceded four goals.
"I have never seen a team more in control as Liverpool were against Bournemouth on Sunday go on to lose. They should have had that game wrapped up and it is something Jurgen Klopp must address.
"Milner has done well this season but if Liverpool are to sustain a challenge, they need another left back and centre back in January."
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