Moyes was labelled 'The Chosen One' when Sir Alex Ferguson recommended the Everton boss as his replacement in 2013 following the end of one of the most iconic management spells in football history.
Moyes only lasted ten months in the job as United slumped down the table, and was replaced by Ryan Giggs on a caretaker basis before Louis van Gaal took over in the summer of 2014.
Evra has recounted how the transition came about in his new book, explaining that the United fear factor quickly evaporated.
"The fear other teams had of us disappeared in a few short months," Evra writes.
"Old Trafford had simply stopped being a fortress. You only had to look at David's face to see the pressure he was under.
"But the way he dealt with it and us was a big mistake. In the dressing room before one game, he said, 'Guys, you've won everything here, you have to show me the way to win. I have never won the league, you have to show me how to do it.'
"I could see what David was trying to do by making the players feel responsible, but Ferguson would never have asked his players how to win a game. He would have told us how to do it.
"Some players used that against him because they thought they were now in charge. Players who'd accepted being on the bench under Ferguson would complain if they were on the bench under Moyes. That made a very hard job even harder."
Evra descirbes how a series of incidents undermined Moyes' authority leading up to a 2-0 defeat to his former side Everton.
Toffees fans abused the team bus post-match, with Giggs losing his cool, which eventually led to a management change.
"On Easter Sunday 2014, we lost 2-0 to Everton. Giggsy, who had been dropped, went mad after that match when Everton fans surrounded our bus and started abusing us," Evra explains.
"One of them threw something that bounced off the coach window. Giggsy stood up on the coach and shouted: 'F***ing Everton fans are now taking the piss out of us. Enough is enough.'
"He was right. The next day, the senior players - myself, Vida [Nemanja Vidic], Wayne [Rooney], Giggsy [Ryan Giggs], Rio [Ferdinand] and Michael Carrick - were summoned to Ed Woodward's office. I think David knew what was happening. Ed spoke to us players separately. I was the last to go in. 'Is David Moyes still the man to lead this team?' he asked.
"'The players are the first people who are responsible,' I replied. 'We are to blame more than the manager, but the dressing room is not a happy place.' 'I know,' said Ed. 'Thank you for your honesty. We will see what decision we take.'
Woodward will leave his post as United's executive vice-chairman at the end of this year, and whether he employs the same method to judge his current predicament remains to be seen.
However, with reports emerging that the likes of Cristiano Ronaldo and Bruno Fernandes have lost faith in Solskjaer, the Norwegian could be on very thin ice indeed.