Solskjaer achieved his aim of guiding United back into UEFA's flagship competition with Sunday's 2-0 win over top-four rivals Leicester City.
The Red Devils looked fatigued in the closing stages of the season, however, with Solskjaer reluctant to deviate away from his preferred starting XI.
Neville believes that a significant upgrade on the current squad is required if United are to challenge on multiple fronts next season.
"They were absolutely done in with 20 minutes to go and that just demonstrates that they need more players in the squad," he told Sky Sports News.
"The last time United finished in the top three they spent £170m under Jose Mourinho that summer and obviously didn't invest it as wisely as they have this last year.
"I think United need to invest that money again but do it correctly this time to get anywhere need Liverpool and [Manchester] City. That squad needs improving."