With midfielders Fabinho and Jordan Henderson being deployed in central defence, Carragher questioned while on Sky Sports how the defenders left on the bench might have reacted.
On Henderson playing at centre-back, he said: "It's almost like having a goalkeeper you don't fully trust.
“Forget Virgil van Dijk and Joe Gomez, they're out. I think No.1 it's imperative Liverpool sign someone in January - that's obvious, I'm not saying anything different.
“But I think the fact they played Jordan Henderson tonight at centre-back it's not going to do a lot for the two lads [Nathaniel Phillips and Rhys Williams] on the bench confidence wise so if he goes back to them how do they feel if there's two midfield players playing there.
"That tells me they're not going to be feeling great if they go back in. Jordan Henderson's not a centre-back. He found it tough today. He done OK, done well considering it's not his position.
"I can't see Liverpool winning the league if they don't bring in a centre-back and I said that on the back Everton vs Liverpool with Van Dijk out. It's going to be very difficult.
"I still think Liverpool have enough quality to go for the title but I think it's a really tough ask."
Williams, 19, has made 10 appearances for the club so far this season, making one Premier League start in the recent win over Tottenham and playing 30 minutes against West Brom.
Phillips, 23, has made three starts in all competitions and they came in the league fixtures against West Ham, Brighton and Newcastle.
Henderson said after Danny Ings scored the only goal of the match: “The start didn’t help.
“We’re starting slow in games and it’s not us. We’re probably saying that a few too many times at the minute so that doesn’t help.”