Sadio Mane's goal and a double off the bench late on from Xherdan Shaqiri handed Liverpool a 3-1 win which returns the Reds to the top of the Premier League.
Jose Mourinho's charges have already tasted defeat five times in 17 Premier League games, conceding 29 goals - the worst defensive record of any team outside the bottom five.
And Keane believes that the players must take the brunt of the blame for that poor form.
"It’s easy to sit here and be critical of players but a lot of the players playing today aren’t good enough to play for Manchester United," the former United captain told Sky Sports.
“Liverpool have dominated everything: corners, possession, shots, goals and I’m not surprised. I did fear the worst today and I think it could’ve been a lot more towards the end.
"Liverpool just toyed with United towards the end. It’s a tough day for United but I’m not surprised.”
Keane also singled out Mourinho's ragged backline as the main culprit, while suggesting that the scoreline flattered his former employers.
"The biggest problem for United is defensively, you have to get some sort of foundation to move forward," he added.
"You’ve got to try and keep some clean sheets, they look like they are all over the place. If Liverpool were really at it today they could have scored four or five.”
United will be back in action next Saturday, when a visit to Cardiff City beckons.
The Red Devils then close out 2018 with back-to-back home games, with Huddersfield and Bournemouth travelling to Old Trafford on December 26 and 30 respectively.