The only remaining fit centre-half, Kolo Toure, was struggling with cramps by the end of the game prompting Klopp to indicate a new defender could be on the agenda this winter.
"In this moment with no centre-back fit I would say it is a situation where we have to think about going into the transfer market," Klopp said.
"Two weeks ago we had three centre-backs, that's a good situation, at the start of the season we had five, now we have none."
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