Van Persie scored a goal in each half on Monday, with the help of some Southampton defensive errors, to secure a fifth consecutive victory and move United up to third in the Premier League table.
It was a largely disjointed display and Van Gaal acknowledged that many of his players under-performed, although this number did not include Dutch countryman Van Persie.
"Not only the goals are telling something about Robin van Persie," Van Gaal told his post-match press conference.
"It think also his [overall] performance - he was one of three players on the pitch for Manchester United who were good or maybe very good.
"He had a great influence on the result so I'm very positive. Until now it is his best performance [this season].
"The second goal was not so easy because the ball is coming for his right foot but he makes it with his left foot. It is a nice touch."
"They were not good. There is a range, of course, between good and bad but they were not good
"Normally you have six, seven or eight who are good and three players who are in that [bad] range.
"Too many players were not good, I believe."
"It's fantastic to be third in the table but I had hoped that we'd do that with a better performance because tonight we were the lucky team."
