Moyes is coming under increasing pressure after being named as Sir Alex Ferguson's successor on a six-year contract in the summer, with United's Premier League title defence effectively over with the Red Devils now 16 points adrift of leaders Chelsea.
Even a top-four finish and a place in the Champions League could be beyond the Red Devils this term, with a nine-point gap to Liverpool needing to be overcome.
Moyes takes his team to title-hopefuls Arsenal on Wednesday night in the Premier League, where a further setback would only add to the criticism currently being aimed in the Scot's direction.
But former United defender Neville, who enjoyed great success in his playing days under Ferguson, believes the North West giants are not in the habit of making hasty decisions.
When asked if Moyes would stay on if United missed out on a Champions League berth, he told L'Equipe: "I prefer to talk about a club that is not like the others, with a different philosophy and that gives time to its managers.
"At Manchester United, hard work always pays off and David Moyes is working a lot.
"Before Alex Ferguson, Tommy Docherty, Dave Sexton and Ron Atkinson also had time. They always got full support.
"David Moyes deserves as much time as his predecessors. Manchester United is not Real Madrid or Chelsea, clubs that sack a manager who has won trophies.
"Manchester United is different and has to remain different and I will repeat that even if they don't qualify for the Champions League."
Moyes' relationship with the media is also coming under scrutiny, with his pre-match press conference prior to the Emirates trip lasting just three minutes.
Neville feels that the former Everton boss must adjust to being in the full glare of the spotlight now that he is at a club with the global reach and stature of United.
He added: "David Moyes also has to understand the full extent of the media coverage of Manchester United, which is completely different than Everton.
"The Manchester United manger is like a head of state - when he speaks, his words are broadcast all over the world in a few seconds.
"Manchester United is a monster that you need to tame. I have always believed the club would change David Moyes and not the other way round."
@solskjaer99: I agree with you mainly about Fergie but I think with Moyes confidence, or a lack of it, is playing some part. I think he's inherited a squad of players loyal to Fergie, bar maybe Rooney on last season's form. As things progress Moyes will hopefully grow in confidence, feel more in control and by signing some more players feel like it's his squad rather than Fergie's. I do point out what I see as flaws with Moyes but remain hopeful for United's future, things will come good, they have to...- shea666