United saw their chances of lifting a piece of silverware this season evaporate after a 2-1 defeat to Arsenal in their FA Cup quarter-final clash on Monday.
Mata meanwhile was an unused substitute in the loss, prompting speculation over his future at the club.
Scholes accepts he understands Van Gaal's system but claims £37million signing Mata's days could be numbered.
"In recent weeks, Van Gaal has tried what I would describe as a more Barcelona-style approach to games," Scholes told the Independent.
"His centre-backs push wide, the full-backs push on and the team pass the ball. It has worked against the weaker teams but it is against the stronger sides, starting with Spurs and the high-pressing game they play, that you have to wonder whether it will be found out.
"To play this way, you really need to be exceptional. Barcelona can do it because they have the players and they have been playing this way for years.
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Juan Mata has become frozen out of Louis van Gaal's plans recently
"United have spent around £220m in the last three transfer windows and yet I would question whether they have the players to operate this system.
"Against Arsenal, there were times when United went more direct to Marouane Fellaini but not as much as might be expected. For what other reason was he in the team?
"At least it gave United a chance to play in their opponents' half. It might be a bit prehistoric, and there is no chance that Van Gaal will want to do it long term, but if United keep playing the way they are, they will be found out against better sides.
"The Spurs midfield, for example, has Nabil Bentaleb and Ryan Mason at the centre, two players I like. They get to the ball quickly and close opponents down. If the aim is to pass around them, then you have to be very polished in that kind of possession-style game.
"My guess is that Michael Carrick will play against Spurs on Sunday, which will help United.
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Paul Scholes thinks Louis van Gaal may have missed a trick in not picking
"I understand what Van Gaal is trying to do. I like that he is playing with the wide players. I also know that as former players we cannot harp on about the old days for ever.
"Things change, although I believe that certain principles, of attacking, entertaining football, should always be protected. Like any other match-going fan - I have two season tickets for Old Trafford - I want to see the team play well and win. I just don't think this system is the best for these players.
"What I find hard to understand is how, in March, United are playing another new style with no evidence that they have the personnel to do it. Managers live and die by their recruitment.
"You buy the right players for the system that you believe will be successful. I don't believe that the club have achieved that balance.
"There must be concerns for Juan Mata, who has not started a league game since the Queen's Park Rangers match on 17 January. Given the system Van Gaal seeks to use, I wonder why Mata does not play instead of Fellaini, especially given that United can be reluctant to knock the ball long."
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