Greenwood, 21, will leave the club by mutual agreement after a six-month internal investigation.
It came after charges against the player, including attempted rape and assault, were dropped in February.
“It was clear from day one that he wouldn’t play for Manchester United again,” said former defender Neville.
Speaking on Sky Sports Monday Night Football, Neville, 48, who made 602 appearances for United, added: “The process in getting there has been pretty horrible. When you have significant situations, and difficult situations like this, it requires strong authoritative leadership. And that comes from the very top. Manchester United don’t have that.”
Fellow pundit and former England midfielder Karen Carney said the matter was “handled poorly” and it was a “really uneasy situation for me”.
England international Greenwood was arrested in January 2022 following allegations surrounding material which was published online.
In a statement, Greenwood accepted he had “made mistakes” and took his “share of responsibility”, but added: “I did not do the things I was accused of.”
United have said “based on the evidence available to us, we have concluded that the material posted online did not provide a full picture and that Mason did not commit the offences in respect of which he was originally charged”, adding: “All those involved, including Mason, recognise the difficulties with him recommencing his career at Manchester United.”
An announcement of the investigation’s results was expected before United’s opening Premier League game of the season against Wolves on 14 August, but the decision was delayed amid fierce debate about Greenwood’s potential reintegration at Old Trafford.
The club said they wanted to consult with their women’s team, some of whom were part of England’s World Cup squad playing in Australia, before announcing a decision about Greenwood’s future.