The result, his heaviest home loss in management, saw renewed calls for the Portuguese to leave following a less than impressive start to the Premier League season allied to underlying problems with executive vice-chairman Ed Woodward and star man Paul Pogba.
But Neville, who of course played his entire United career under only one manager, thinks the club should stick to their guns.
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"We saw Louis van Gaal sacked after an FA Cup final victory, we saw David Moyes sacked with four games to go of a season, so we are no longer talking about a football club that is behaving as it has historically done," he told Sky Sports Monday Night Football.
"I accept these are different times and I accept the difficulties and challenges, but my honest view as I stand here now is that Ed Woodward gave him a contract last season, only seven or eight months ago, and he should see that contract through to the end and do the job.
"You can't keep jumping around with managers. I hear the third-year Mourinho stories and all the rest of it and you can't disagree with those stories because there is some history.
"But what I would say is it's time now for Manchester United to batten down the hatches and for Jose Mourinho and Ed Woodward to sort themselves out if there is a problem there.
"Get the team right for the rest of the season because the club is bigger than any individual. They have to get themselves sorted because it's not a time for in-fighting and politics."
Mourinho endured a particularly spiky press conference after the game, a game which left the side 13th in the table with just one win from their opening three matches.
"We lost a game because we conceded a goal from the first corner of the match against us," he said. "In the first half zero corners, zero free-kicks, on minute 50-something they had one corner and scored a goal, and you want, with that goal, you want to transform the story of the game.
"But don't lose your time. Today I had the proof the best judge in football are the supporters."
The Portuguese then went on the offensive, suggesting those in the media questioning him were orchestrating a campaign.
"Keep trying. Keep trying. Keep trying. We lost last season here against Sevilla and were booed because we deserved it, because we were not good," he said. "Today the players left the pitch after losing at home and they were applauded because they deserved it.
"So keep trying. Do you know what was the result? Three-nil. Do you know what this means (holding up three fingers)?
"Three-nil but it also means three Premier Leagues and I won more alone than the other 19 managers together. Three for me and two for them."
Mourinho then left his seat repeating "respect, respect, respect" as he walked out of the press conference.
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