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.
Man who escaped from Winfield Correctional Facility captured
Herzet said a lot of manpower was needed because of earlier statements made by Mitchell that he wouldn't be taken alive. Sheriff Herzet said Mitchell would be booked into the Butler County jail for aggravated escape from custody.
"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.