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Phelan, 53, was promoted from assistant boss to caretaker manager when Steve Bruce resigned in July.
Despite a threadbare squad, he has a 100% Premier League record with wins over Leicester and Swansea.
"He can handle the situation at Hull and the players are playing for him," Neville told BBC's Match of the Day.
Phelan chose not to make a substitution last week and only made one in the 2-0 victory against Swansea, bringing on Shaun Maloney, who scored the opening goal.
Hull are yet to make their first signing of the summer transfer window, despite the departure of several members of last season's promotion-winning squad and a long injury list.
Phelan worked under Sir Alex Ferguson for 12 years, having served as a first-team coach from 2001 and assistant manager from 2008-2013.
Neville said that experience means he is equipped to deal with the pressure at Hull.
If you talk about someone who deserves the opportunity then it's Mick Phelan
"He's done an incredible job so far," added Neville, who was part of the United squad when Phelan was on the coaching staff.
"Mick's galvanised that team spirit. They've had a horrendous pre-season. They've got no squad and he's had kids on the bench.
"If you talk about someone who deserves the opportunity then it's Mick Phelan."
Hull's win over Swansea, which took them third in the table, was sealed by an injury-time goal from Abel Hernandez.
The away fans at the Liberty Stadium chanted 'we want Phelan in' but he knows he must continue to win matches if he is to get the job on a full-time basis.
He said: "It was nice to hear them singing that - it's better than hearing them singing 'we want Phelan out'.
"I think everyone knows we have decisions to make on my future, the future of the staff and the ownership."
Hull City should give Mike Phelan the manager's job on a full-time basis, former England defender Phil Neville told BBC's Match of the Day.