Robin van Persie capitalised on defensive lapses from the home team in each half to help United chalk up a fifth consecutive victory despite a ragged display.
And Van Gaal, whose team now lie third in the table, refused to let his compatriot's goals mask his concerns surrounding United’s general play.
He told Sky Sports: "We lost the ball too easily in the first half, I think. We didn't have good positional play.
"The only chances that Southampton created were when we lost the ball. That was not good, despite our good result. We got a present from Southampton
"We needed confidence on the ball, which we didn't have - I said that at half-time.
"I think Southampton played better than Manchester United but we were the lucky guys.
"I want them to show the confidence that we have shown on the training ground - this week we have trained fantastically.
"But I I didn't see it on the matchday and that’s the most important hour. You have to show yourself on the matchday."
One player certainly lacking in fortune was United defender Paddy McNair.
The 19-year-old endured a torrid time under first-half pressure from Southampton and Van Gaal replaced him with midfielder Ander Herrera in the 39th minute.
Van Gaal conceded it was a tough decision to make but maintained he was looking out for McNair's best interests.
He added: "He had not any confidence. He had already given three big chances away.
"It's very disappointing for me and also for Paddy but I had to because as a manager I am responsible [for the] win.
"After the change we played a little bit better. Of course it is tough but it is also in his best interests.
"I have made a lot of [early] changes and all the boys can survive. It is only one moment in their lifetime."
