The Red Devils spent a world-record fee on Paul Pogba last summer, in addition to bringing in Zlatan Ibrahimovic, Henrikh Mkhitaryan, Eric Bailly and manager Jose Mourinho, but they remain outside the Premier League's top four.
United have been linked with moves for the likes of Antoine Griezmann, Victor Lindelof and Tiemoue Bakayoko when the transfer window reopens this summer, and Neville believes that there are a number of areas that need addressing.
"I think you could argue they need strengthening in defence, midfield and attack. Three or four players wouldn't just be in one area, they would be spread among those," he told Omnisport.
"They do need strengthening. It's obvious. I don't think United have sat there as the only team that needs strengthening. If you think about English teams falling short in Europe, we need to strengthen all our top teams. [Manchester] City need to strengthen, Arsenal, Liverpool, United need to strengthen.
"I don't think United are in a unique position. The issue I suppose is that every club seems to be after the same players."
United's victory over Middlesbrough on Sunday takes them to within four points of the Champions League places, with two games in hand over fourth-placed Liverpool.