Allardyce labelled Van Gaal's side as "long-ball United" following Sunday's 1-1 Premier League draw at Upton Park.
That prompted a reaction from the Dutchman, who produced a dossier ahead of Wednesday's match with Burnley claiming that Allardyce's assertion was incorrect and that it was West Ham who had a higher percentage of long balls.
Scholes, who the Premier League on 11 occasions with United, believes Van Gaal should not have risen to Allardyce's comments - which he felt were said in jest.
"Why would you react to a West Ham manager? It's different if it's a rival manager like Chelsea or Manchester City's, but at the end of the day you're the Manchester United manager," he told BT Sport.
"I found it all bizarre to be honest with you, as I felt Allardyce's comments were light-hearted in the first place."
Former Netherlands international Pierre van Hooijdonk had a similarly dim view of his compatriot's tenure at Old Trafford, describing his impact at the club as "unrecognisable".
The ex-Celtic and Nottingham Forest striker also claimed that "the biggest clowns" are making a mockery of Van Gaal's tactics.
"Louis looked like a suitable successor for David Moyes but, at the moment, he is disappointing," he told Voetbal International.
"To steer away from the results, the way they are playing is awful. I can't see the touch of Van Gaal - he is unrecognisable.
"It all started in the summer. You couldn't follow their transfer policy. It looks like United just bought some great names. The result is a team of top players without any unity.
"Even the biggest clowns are laughing about Van Gaal. During my spell at Nottingham Forest I've worked with them: Dave Bassett and Ron Atkinson.
"In England they're respected coaches, but I know they are just really bad actors, men that had no idea how to improve a team. These guys and [Sam] Allardyce as well."
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