"It is always like that when you lose a game, certainly in the last minute, that you are fed up. How we have played (against Southampton) is not always the main issue because you can play badly and win.
"When that happens, you are not so fed up. But we have played very well and lost, like Chelsea away last season, so when that happens you are more fed up than ever."
Asked if he had offered his resignation to United chief Ed Woodward, Van Gaal replied: "I have not mentioned that, ever.
"(Woodward's support) is fantastic of course, but that also gives you a lot of pressure. When the board has such confidence, the pressure is much higher than when they say it is the last game.
"When your confidence is not so high, you can fight against it."