The Red Devils had taken the lead against PSV Eindhoven through Memphis Depay, but the Dutch side recorded a famous win after Hector Moreno and Luciano Narsingh netted.
"We can only blame ourselves, I think, because we created so many chances," Van Gaal said after the match.
"After Tottenham I said you have to score one more than the opponent. PSV were very effective, scoring from nothing ... a corner kick, a deflected ball, then scoring in the second half from a poor pass.
“We have dominated the game and had most of the chances. But we have lost. It's fantastic for PSV and their fans but we have lost."
United suffered further bad luck with news that Luke Shaw had broken his leg in the game.