"I watched Manchester City [on Sunday], where Manchester United are trying to get to in terms of getting to the top of the Premier League with Liverpool. Bernardo Silva, Raheem Sterling, Kevin De Bruyne, David Silva — far better players than in that Manchester United dressing room who work twice as hard.
"Everton ran 4km further in the first half. Everton? You die for every single inch on the pitch. It's embarrassing just watching some of the players out there. I'm absolutely furious. That performance was rancid."
Neville refused to name players he believes are underperforming and is worried United will struggle to rebuild under the current hierarchy.
"Forget talent. If you don't work hard and don't run around in that shirt, get rid of them. I'm watching players for Manchester City and Liverpool work their backsides off every week and I'm watching Manchester United players walk around, jaunt about, jogging back.
"I don't mind them losing games or conceding goals, but you do not drop below the standard of work ethic expected at that club, and they are falling below it."
The appointment of Solskjaer on a permanent basis after an impressive spell as caretaker manager won widespread approval from Old Trafford veterans. He mostly retains their confidence but the feeling towards some of the current squad is toxic.
"I reckon the more Solskjaer's watching those players, the more he will be losing faith because they are letting him and that club down," Neville added. "I am concerned. This idea that Manchester United only won the league a few years ago is gone. They are in the wilderness. Seven years [since being champions]. Where do you see the next league title coming from? Things can be turned around quickly, but big decisions, good decisions don't come around quickly.
"Solskjaer spoke about rebuilding the squad. But who is rebuilding this squad for Ole Gunnar Solskjaer, for the Manchester United fans? I don't think there is anyone there to rebuild that club from a football point of view. Something is fundamentally wrong."
Michael Owen was also unimpressed with United's showing.
"I know we should praise Everton but I think the story of the game is how bad United were," said the former United striker.
Former midfielder Paul Ince wondered whether the sudden downturn in United's performances might threaten Solskjaer's future.
"The way United are performing right now, you have to ask if Solskjaer is the right man," Ince said. "You cannot be getting embarrassed at Goodison Park like this."
And he had harsh words for Anthony Martial over his defending for Everton's third goal from Digne.
"It came through a lot of bodies so I'm not sure David de Gea could do much with that, but I'm more concerned with Anthony Martial. He just turns his back on the ball and that would not have happened in Fergie's [Sir Alex Ferguson's] era. You would have got anything you could behind the ball when Sir Alex was in charge."
Former Liverpool defender Jamie Carragher was also scathing.
"That was the worst performance from a Manchester United team I have seen since I've been working for Sky."