The Old Trafford hierarchy will wait until the end of the season to appoint a permanent successor to Mourinho, who was sacked on Tuesday after 144 games in charge across two-and-a-half years.
A caretaker boss will be installed for the rest of the campaign but come decision time Neville feels United must go for Tottenham boss Pochettino.
He told Sky Sports News: "The consequence of not backing your manager or going against your manager for one or two signings… it never ends well.
"It is never as simple as just being the manager's problems.
"The players take responsibility, the board takes responsibility.
"There's been seven years of poor decisions and poor resentments.
"Who has the final say? I can't see anyone in the football club with the qualification to do that.
"Recruitment has been erratic.
"The club needs to reset and take stock of what they are doing.
"That is not about speed, it is about making sure the next manager is the right manager.
"They are going to have to pay for him probably.
"They are going to have to put the right structure around him.
"They have got to put more intelligent people in there and not hide behind the manager.
"They (players) can no longer blame the manager. That excuse has now gone.
"I said last season the next manager should be Pochettino.
"You look at his belief in young players at Southampton and Tottenham, how he carries himself in public and private.
"For me he feels the most ideal candidate.
"United have tried managers who have won European cups, leagues, solid grounding in Premier League.
"Three key principles of this club are promotion of youth, attractive football and winning football.
"I do think he is the person who is the most outstanding candidate.
"If you're Daniel Levy you grab him and hold on for dear life as you move into a new stadium."
Earlier this month SunSport reported that United were prepared to part with the £40m required to bring Pochettino to Old Trafford.
After enjoying great success with Espanyol and Southampton, the Argentine moved to Tottenham in 2014 and has transformed the team into a genuine force in the Premier League.
In four-and-a-half seasons he successfully guided the club back into the Champions League on three occasions and to the Carabao Cup final – though he is yet to win a major trophy as a coach.
Central to his success has been the regular blooding of young players from the Spurs academy, with spending in the transfer market having been limited due to the club's inferior resources.
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