The Swans chief says his side grounded Van Gaal, and warned the Red Devils that they must sign a number of new players before the end August or risk finishing mid-table
The Swans won 2-1 at Old Trafford on Saturday in Van Gaal's first competitive game in charge since replacing David Moyes.
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"I had a great day! United thought they signed a giant with Van Gaal, but we really showed them on Saturday," he told NOS. "I saw scarfs and banners with his face all over town."
"We played a really good match and deserved the three points. I have a lot of respect for Van Gaal, but we put him with both feet on the ground.
"I mean, if you have a mediocre squad like United, it's going to be tough. I really hope for Van Gaal that they sign some players, because with this team they will end in the middle of the table."
The Red Devils have been linked with a hst of players this summer, and hope to conclude deals for Sporting defender Marcos Rojo, Ajax's Daley Blind and Fiorentina winger Juan Cuadrado.
Roma centre-back Mehdi Benatia has also emerged as a serious target since Saturday's defeat, according to reports, though there are further rumours that Bayern Munich could step in and secure the Moroccan's signature.