The Scot was dismissed on Tuesday after nearly 10 months in charge at Old Trafford which have seen the club go from being Barclays Premier League champions to failing to qualify for next season's Champions League.
Reports of Moyes' imminent departure emerged on Monday afternoon and Neville was sad that the Scot's exit proved to be an undignified one.
"The last 15, 16 hours or however long it's been, I don't like it, it's not the way in which the club should portray itself," the former right-back, who won eight Premier League titles with United, told Sky Sports News.
"But it's the modern world, it's how things seem to be dealt with now, but I'm a traditionalist and I think it could have been dealt with a whole lot better.
"I believe in managers being given time, I think they should be allowed to complete their work. The idea of giving people three and four and six-year contracts and then getting rid of them after 10 months is something that's foreign to me.
"However, there's no disguising that the football this season has been poor, the results have been poor, as a fan I've not enjoyed watching it - I'm sure David Moyes himself hasn't enjoyed watching it.
"And I can't think many Manchester United fans will have enjoyed watching it either.
"The performances have sort of got worse and worse. There was a little bit of a pick-up before Christmas when you thought there might be a bit of a run but in the last month or two the performances have sort of deteriorated really."
He added: "The players have to take massive responsibility.
"I never once during my 17/18-year career at United turned around after a game and thought 'you lost us that game boss'.
"It's always the players. Players have to take responsibility, accountability in football.
"Those players there are not as bad as they have been showing, I've played with a lot of those players
"They've got great care for United, they love the club - the ones that I know - they're desperate to do well for the club and they have completely lost confidence.
"These are players who were champions nine months ago and the decline has been surprising to say the least."
One of the players in the dressing room Neville knows best is Ryan Giggs and the Welshman will now take charge of United until the end of the season.
Moyes' predecessor Sir Alex Ferguson spent nearly 27 years in charge at United and brought both Giggs and Neville into the team after initially struggling to make an impact at Old Trafford.
Neville played with Giggs throughout his entire career at United under the Scot and the England coach believes his former team-mate is entering the lion's den, with management now being a largely thankless task.
"It's a different world to the one it was in the 1980s when (Dave) Sexton, (Ron) Atkinson and Sir Alex Ferguson were given time through their difficult moments," he said.
"That's just not going to happen any more. It's something that I don't like about the modern game, the fact that managers get sacked every 12 months. It doesn't matter whether it's my club, it's United, or any other club.
"I genuinely believe there is a lack of decency now in the way in which football managers get dealt with at all the different clubs.
"They're just so much in the firing line and they accept it's a pressurised job, they get well paid for it, but I think there is a way of decency with dealing with people.
"Football managers now just get tossed around, chucked about, disregarded, rubbished. Decent men, good men just get thrown away and that's not just David Moyes, that's all the way through football."
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- David Moyes
- Barclays Premier League