A toothless United performance was punished with 21 minutes remaining in Sunday's game when Dusan Tadic steered in the winning goal to ensure Southampton leapfrogged Van Gaal's men into third in the Premier League.
The hosts failed to muster an attempt on target in the defeat, but Van Gaal felt his side dominated proceedings.
Despite losing at home in the Premier League for the first time since the opening day of the season, the Dutchman asserted his view that the visitors were rewarded for playing cautiously.
"We didn't create so many chances, despite dominating the game. We gave them a chance in the first minute but dominated after that," he told Sky Sports.
"We had three big chances, but it was not enough.
"Southampton were well organised, defended well but they came for a draw, I believe, and they go away with a win, which is disappointing.
"[Juan] Mata had three chances, but you cannot change the result. We gave the goal away. Football is game from mistakes."
Captain Wayne Rooney echoed his manager's views, stating United deserved to take maximum points.
"We deserved to win, but that's football," he added.
"We've been punished for not taking our chances. We have to move on and focus on the next game."
