Tottenham's Australian head coach, Ange Postecoglou, may have his issues at the London club but they pale beside the travails of United's Dutch coach, Erik ten Haag, whose future at the former European champions will be under fresh scrutiny.
Brennan Johnson had fired Spurs into the lead after only three minutes before United captain Bruno Fernandes was shown a straight red card just ahead of half-time after a sliding challenge on James Maddison.
Spurs doubled their lead soon after the restart through Dejan Kulusevski, before Dominic Solanke ended any hopes of a United comeback when he scored a third with 13 minutes left.
Neville said on Sky Sports: "It was an absolutely disgusting performance in that first half in effort, quality, everything you would want in a football team.
"There will be a lot of questions to answer for that group (of players) and the manager in the next week.
"The pressure is going to get ramped up this week - it is going to be brutal. It has been a bad day for Ten Hag, really bad.
"It's one of the worst performances I have seen under Ten Hag - and that is saying something. It is really bad."
Ten Hag disagreed with the dismissal of his captain. "I don't think it is a red card," he said.
"It was a bad start of the game, Tottenham were dominant, we could not get the right press and also made many mistakes in possession, we could not find the spare man or pass over the press or made wrong decisions.
"But we could have come back in the game, because we had our chances. Then the red card, of course, that changes the game."
Looking forward, Ten Hag added: "It's always a new day and I told them in the dressing room 'come on, tomorrow's a new day'. But we definitely have to learn, make things better."
Postecoglou felt his side were good value for their victory, despite United's shortcomings. "We were real good. Obviously it is a great victory.
"I thought the manner of the performance, we played our football really aggressively. That is everything we want to be.
"I could see the boys' attitude, they were not dwelling on missed chances. I knew the goals would come. We should have probably had a couple more."
In Sunday's other EPL match, Aston Villa missed the chance to move level on points with leaders Liverpool after a 2-2 draw at Ipswich.
Liam Delap scored twice for newly-promoted Ipswich to earn a point at Portman Road.
Villa had led 2-1 at half-time, but Delap's goal in the 72nd minute  ensured the points were shared.
Villa remained in fifth place and Ipswich are 15th after a fourth straight draw in the league.
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