Jurgen Klopp’s men won 5-0 at Old Trafford in October and expectations of a similar rout were well-founded as Liverpool exposed the massive gulf between the sides with Mohamed Salah scoring twice and Luis Diaz and Sadio Mane also on target.
Liverpool move two points ahead of Manchester City at the top of the table, but still need the English champions to slip up in their remaining seven league games of the season to win the title.
Rangnick will step aside at the end of the season, with Ajax manager Erik ten Hag reportedly set to take over.
And the German said the impact Klopp has made on transforming Liverpool’s fortunes is the example for United to follow.
“It is embarrassing, it is disappointing, maybe even humiliating,” said Rangnick.
“We have to accept they are six years ahead of us now. When Jurgen Klopp came they changed at the club and lifted not just the team but the club and city to a new level.
“That is what needs to happen with us in the next transfer windows.”
In contrast to the fine margins separating Liverpool and City, a 22-point gap now lies between the league leaders and United in sixth with only Tottenham and Arsenal’s own failings keeping the Red Devils in the race to qualify for next season’s Champions League.
Rangnick’s attempt to plug the holes in the United defence was a recall for Phil Jones, making just his second Premier League appearance since January 2020, as part of a back five.
But it took just five minutes for the visitors to be cut open.
Mane’s through ball picked out Salah in acres of space and he found Diaz to apply a simple finish from close range.
“They always try to give us the ball in a one-against-one situations, so it makes our life much easier,” said Salah.
– Support for Ronaldo –
Two minutes later the fierce rivalry between English football’s two most successful clubs was set aside in a show of support for Cristiano Ronaldo.
The Portuguese superstar was missing for United after revealing on Monday that his newborn baby son had died.
Supporters on all sides of Anfield stood for a minute’s applause, while the Liverpool fans sang their own anthem “You’ll never walk alone”.
“That was my moment of the game,” said Klopp. “So many things are much more important in life than football, we feel for Cristiano and his family.”
On the field, the one-way traffic continued with United barely able to get out of their own half.
A second Liverpool goal seemed inevitable and when it arrived, it was of the highest quality.
Joel Matip fizzed the ball into Mane’s feet and the Senegalese lofted a first-time pass over the top for Salah.
The Egyptian had not scored for Liverpool from open play since February, but showed no signs of a lack of confidence as he cushioned the ball into his path and slotted low past David de Gea.
Half-time offered United some respite and they improved markedly after the break thanks to the introduction of Jadon Sancho.
But Liverpool were still the lethal side in attack as Mane coolly steered home the third from Diaz’s cross to end any hope of a United revival.
Salah then took his tally for the season to 30, five of which have come in two games against United, as he lifted the ball over De Gea from Diogo Jota’s pass five minutes from time.