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."
Although he would not name the other two players he earmarked for praise alongside Van Persie, Van Gaal was clear that he expects far higher quality team performances from United.
"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."
