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."
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."
