Manager David Moyes paid the price for United's dismal season last month, losing his job less than a year after being appointed as Alex Ferguson's successor.
However, Neville has pointed to a deeper problem, claiming too few of the players recently bought by the Old Trafford club have been good enough.
He believes United should back their youth academy graduates - such as James Wilson - rather than bring in second-tier signings.
"United have panicked into signing players who were not their top choices," the 39-year-old said.
"It was quite public last summer who United's targets were – it was either (Gareth) Bale or (Cristiano) Ronaldo, it was (Cesc) Fabregas, it was (Leighton) Baines and it was (Marouane) Fellaini (only the latter joined the club).
"They were the targets, it was publicised – and I don't know why because Manchester United have always kept their transfer dealings really quiet. I'm not quite sure how all of a sudden everyone knows who they are signing.
"But if they can't get number one, number two, three, four, I'm not in a rush.
"As a Manchester United fan, I'd rather see James Wilson come through than some fourth-choice striker who isn't at the top of the list.
"I don't want signing number eight, nine, 10 because they can't get number one, two, three, four, five, six, seven. I have no interest in that."
Neville hopes Louis van Gaal, who is expected to be United's manager next season, will focus on quality over quantity when looking to sign new players.
"If he (Van Gaal) decides he wants eight players, that doesn't mean he should go and buy eight players," Neville said.
"Signing three or four real top-quality (players) – and improving next season, bedding them in and then going again with two or three more the year after is the organic approach I would expect Manchester United to have.
"However, I didn't expect Manchester United to sack a manager after 10 months, so what's going to happen in the next few months, who knows?"
