Prior to the Red Devils' fixture against rivals Liverpool at the weekend, some Man United fans broke past security again, after also finding their way into the Carrington training ground last week, which resulted in the Premier League fixture being cancelled.
The supporters are angry at the Glazer family's ownership of the club, and their frustrations were compounded by the European Super League agreement the club signed last month.
Speaking to Sky Sports News, Neville said: "This is a consequence of the Manchester United owners' actions two weeks ago. There is a general distrust and dislike of the owners, but they weren't protesting two or three weeks ago.
"The Glazer family are struggling to meet the financial requirements at this club and the fans are saying that their time is up. My view is quite simply that they're going to make a fortune if they sell the club and if they were to put it up for sale now I think the time would be right, and it would be the honourable thing to do.
"There's huge discontent, not just across Manchester United fans, but I think for football fans up and down the country and I think they are just saying enough is enough. The Glazer family have been resilient and stubborn for many, many years. I think they are struggling to meet the financial demands that this club needs and have done for some time."
Neville made reference to the fall Man United have suffered in recent times, being without a Premier League title since the 2012-13 season.
"If you think about the club they picked up in 2004, it had the best stadium in the country, one of the best in Europe, it had the best training ground in this country, and probably one of the best in Europe. It had a team that was consistently getting to Champions League quarter-finals, semi-finals and finals regularly and winning the league every season or every other season," he added.
"If you look at the club now, this stadium I know it looks great here but if you go behind the scenes it is rusting and rotten. If you look at the training ground it's probably not even the top five in this country, they haven't got to a Champions League semi-final for 10 years.
"We haven't won a league here at Manchester United for eight years. The land around the ground is undeveloped, dormant and derelict while every other club seems to be developing the facilities and the fan experience.
"All football fans should unite today behind what Manchester United fans have done today because what happened two weeks ago was really dangerous for English football."
The fixture against Liverpool is yet to be rearranged with Ole Gunnar Solskjaer's side set to face Roma in their second-leg Europa League semi-final tie on Thursday.