Liverpool went on to draw the game 3-3, with Miguel Britos equalising in added time for Marco Silva's side.
Redknapp said: "I look at that Liverpool back four and there's a reason why they concede so many goals because they're disorganised and they have no leaders at the back".
Liverpool have heavy interest in Southampton centre-back Van Dijk, who has handed in a transfer request, but Carragher believes his former club have fundamental flaws in their defensive set-up, which signing £60million-rated Van Dijk alone will not fix.
That's what happened on the first goal - it comes from a counter-attack.
Redknapp was adamant that a van Dijk who is willing to head the ball can rectify matters, but Carra was having none of it.
However, Carragher disagreed: "On set pieces it's not about the defenders".
Stoke City, Burnley, Arsenal, West Ham United, Hull City, AFC Bournemouth, West Bromwich Albion, Swansea: these are all teams that came to Old Trafford last season and somehow left with a point, despite being dominated all game. The way Liverpool are set up - set piece wise - they will always concede goals.
"I think Manchester United will be in there, they didn't make the top four previous year but I think they will with the additions that they've made", he said.
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"If you want to challenge for the Premier League, or win the Premier League, you've got to be conceding less than a goal a game: 30, 35 goals".
Liverpool will take on Hoffenheim later this month for a place in the group stage of Europe's elite club competition.
And Redknapp thinks Liverpool should stump up the cash for the centre-half in order to improve their defensive problems. "They need a leader to head that ball clear".
I think everybody's missed this mischievous "friendship".
"Talk about Van Dijk coming in, okay he's a good player, but it's from the side of the pitch, it's the way Liverpool are set up".
"I think (Virgil) Van Dijk's agent has got another 20 grand a week on his contract", said Redknapp.
"Hopefully he'd make a difference on set-pieces, he's a bit taller, but if he was playing today instead or Lovren of Matip, he'd have been in their position".
Hit the video at the top to watch the heated debate.