Van Dijk's campaign is reportedly over after just five games after he suffered a serious ACL injury in the weekend's Merseyside derby, following a shocking tackle from Everton goalkeeper Jordan Pickford.
Carragher admits it's a huge loss for the Reds and believes it could well hand the Premier League title to rivals Manchester City.
But the Anfield icon insists Jurgen Klopp's side can still defend their title as long as they land a world-class centre-back in January.
He believes RB Leipzig's Dayot Upamecano is the perfect fit, and has explained why it's key the Reds act early as soon as the window re-opens to get their man.
"Liverpool's next big signing had to be a centre-back anyway and I am talking next summer," Carragher said on Sky Sports' Monday Night Football.
"Dejan Lovren went and they didn't replace him so they only have three centre-backs and one of those, Joel Matip, is always injured.
"There are question marks now about Joe Gomez.
"So there is no doubt that Liverpool had to go big in the transfer market next summer. That was the next one. That has now got to be brought forward to January 1st, whoever the target was in the summer. Not the end of January. Not [wasting time that month] negotiating with a club."
With so many top clubs looking for quality at the back, Upamecano's name has come up a lot in the transfer rumours mill over the last year or so.
The 21-year-old has been linked with moves to Arsenal and Manchester United in the Premier League after his impressive emergence in Germany.
He played a key role in the Bundesliga side's run to the Champions League semi-finals last season, and was even named man-of-the-match for Leipzig's quarter-final win over Atletico Madrid.
And Carragher has urged Liverpool not to waste time and snap up the in-demand star at the soonest opportunity - even if it means spending top dollar.
"There is a young man everyone was talking about at Leipzig, Dayot Upamecano, there is talk of him. Whether he has the profile of Van Dijk, I think he is only 6'1″ or 6'2″, so he is maybe not that aerial, but if he is the one they wanted then bring it forward.
"Pay extra money and do it on January 1st.
"That means getting through 11 league games without Virgil van Dijk.
"One thing to say about Virgil van Dijk is that in the last 23 games they have only kept five clean sheets, and Van Dijk played all of them, so it is not like everything was perfect. We saw the seven against Aston Villa and we saw the Leeds game.
"But I think they have to go big with a signing."
If a replacement for Van Dijk comes to Anfield this season, Carragher believes it will resurrect the club's hopes of defending their title.
The Reds have endured a mixed start to the season, with three wins, one defeat - an a big one, at that - and one draw in their opening five games.
But Carragher believes the unpredictability of the Premier League this season means the Reds will not have to reach the same level of the last two years to reclaim their crown.
"The good news for Liverpool is that this season you will not need 99 points to win the league," the legend added.
"I think it is going to be in the eighties. Liverpool and City have already dropped five points. For it to be another 99-point season you can only afford to drop another 10 and that is not going to happen.
"So Liverpool have dropped from a 98 average for the last two seasons, but if they drop 10 to 12 points, even 15 from there, they will be there or thereabouts for the season."
Liverpool legend Jamie Carragher has urged the club to sign a first-class replacement for Virgil van Dijk in January after losing their defensive rock for the season with a knee injury.