United claimed bragging rights and consolidated third position in the table after routing reigning champions Manchester City 4-2 in the Manchester derby at Old Trafford - the club's first derby win since 2012.
Goals from Ashley Young, Marouane Fellaini, Juan Mata and Chris Smalling cancelled out City's eighth-minute opener via Sergio Aguero, who netted a consolation in the final minute of regulation time, as United moved four points clear of their neighbours with six matches remaining.
Having chalked up impressive victories over City, Liverpool and Tottenham in the past month, Neville said United can mount a serious title bid if they can improve on losses to Swansea City, Sunderland and Leicester City.
"Next season, [Van Gaal] will look at games he's dropped points in in this season and will think because that level of performance has come now, they could win those games next season," Neville said via Sky Sports' Super Sunday.
"I think the confidence will be growing in the camp. There are people in that dressing room who have won titles, and they'll get the feeling again that the performance levels and confidence is coming back.
"That's the first time Louis van Gaal, Juan Mata and Marouane Fellaini have seen Old Trafford properly today in terms of an atmosphere.
"It's what Manchester United can create and that will give them enormous confidence. It always does when you win big matches."
Neville added: "They're getting so confident now. It is a fantastic four performances.
"Against Spurs, you were maybe saying: 'Spurs were poor that day, they were flaky.' So you were thinking: 'Is that the real deal?'
"To go to Anfield and win makes you really sit up, because it's a tough place to play no matter how Liverpool are playing, what point in the season it is, or what point Liverpool or United are in in their development.
"But to come here today, especially after City started well and went a goal up, that's a proper performance."
