A run of four games in all competitions without a victory put pressure on Mourinho, who came under increased scrutiny before the game, with the Daily Mirror reporting that he would be sacked regardless of the result on Saturday.
As usual, Neville was working for Sky Sports during Brighton's 1-0 win over West Ham and after the game, Kelly Cates asked the former Manchester United defender if sacking Mourinho would be the right decision from the United board.
"No, I think we have enough potential to do better than what we are doing in the Premier League", he said at his press conference, which was scheduled at the earlier than usual time of 8am.
Mourinho was angered by a lack of investment in his squad during the summer, when the club failed to sign a top-class centre-half, and he has also been irked by the absence of support following public spats with star players Paul Pogba and Anthony Martial. I've got to stand up and say "I'm not good enough to do this". "The whole football club of late has been embarrassing".
"Because", Neville added, "if this is true and it's broken the day before it's going to happen and he's going to be sacked after the game or at the weekend it's an absolute disgrace".
"I'm reacting maybe a little bit emotionally, but I don't really care, to be honest with you". Any manager would struggle in that football club in the way in which the recruitment is handled, how it operates. It's the life I love.
The club is "rotten to the core".
Club chiefs believe he would lift the atmosphere at the club, with star man Paul Pogba particularly keen to play under the French World Cup victor.
Yes, he lost his way at Arsenal towards the end, but that should in no way overshadow the fact that he changed the whole ethos of the club, from the development and trust in his younger players to the eye-catching and attractive brand of football he brought to the Gunners.
"The people in the boardroom at this moment in time who are, if you like, overseeing the football operation, are nowhere near good enough".