Shaw: Manchester United too relaxed since League Cup triumph
United travelled to Anfield on an 11-match unbeaten streak but suffered the club's worst defeat since losing 7-0 to Wolves in 1931.
The defeat came a week after United claimed their first trophy since 2017 by winning the League Cup, having beaten Newcastle United in the final.
"It was completely unacceptable," Shaw told MUTV. "Our standards have clearly dropped since we won that trophy, and in the last couple of games we haven't been our normal selves."
United conceded six of the seven goals in the second half as Cody Gakpo, Darwin Nunez and Mohamed Salah all scored twice for Liverpool.
"We need to find the good things we were doing before and bring them back because this hurts a lot, and it's really unacceptable what we did in that second half," Shaw added. "We showed no personality and no mentality."
Former United captain and Sky Sports pundit Roy Keane said the players got carried away by their League Cup success.
"I see the players come here today in the second half, having a laugh and a joke. They're 1-0 down at Anfield and they're having a laugh and a joke with the Anfield staff, goalkeeping coach. I don't like to see all that rubbish.
"I think that circus can creep back in, and the manager and senior players have to keep an eye on that."
Former United captain and Sky Sports pundit Gary Neville described the defeat as a "shambles".
"They've not understood the dangers of this fixture. The Manchester United players have been eaten alive out there," Neville added.