Neville dismayed by United approach
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."
Dwight Yorke also played in the treble-winning team of 1999 and the former striker believes Giggs could be just the man to take the job permanently.
"I know there's a lot of people speculating that they need somebody with big experience out there that has managed a club at the very top level but we are talking about a continuity, something like what Sir Alex Ferguson did," he said.
"There is never going to be someone like Sir Alex Ferguson but what we're given here is a young manager who is looking to break in.
"He's not got the managerial skills but we thought that David Moyes had those skills of going into Manchester United with the experience that he had for 11 years being at Everton and the wonderful job that he'd done but he hasn't been able to turn things over at Manchester United.
"I think for togetherness and getting the results and playing a certain way, a brand of football that is more eye-catching, the Man United way, I feel that Ryan Giggs is the right person."
Real Madrid boss Carlo Ancelotti has been touted as a possible successor to Moyes.
Speaking ahead of his side's Champions League semi-final meeting with Bayern Munich, the Italian said: "I feel sorry for David Moyes, but that's the life of a football coach, sometimes it doesn't go well for you and you are sacked.
"I'm sure Moyes is going to get another team and another opportunity, but I always feel bad when a coach is sacked.
"I am a little surprised because Manchester United don't normally do this."
Former United captain Roy Keane said the current squad and the club hierarchy needed to take a long look in the mirror after Moyes' disappointing reign.
" He certainly had a hard start but I'd look at the chief executive (Ed Woodward), he didn't get the deals done," Keane said on ITV.
"I think it's a shame, he should have been given more time. Some of the players should be ashamed of themselves, they really let him down."
Asked how much responsibility belonged to Ferguson for picking Moyes, Keane added: " I wouldn't say that it was his pick. He certainly put his name forward but the club have to make a decision so you can't be critical of Sir Alex.
"For David Moyes seventh in the league is disappointing but you need people around you, the support, and I don't think he's had that, certainly from the players."
Speaking ahead of Chelsea's Champions League semi-final tie away to Atletico Madrid, Jose Mourinho said: " I feel sorry for David, like I feel sorry for every manager who loses his job."