Van Gaal's third reign ended after a penalty shootout after his side came back from 2-0 down to draw 2-2 with two late goals from Wout Weghorst before Argentina came through the shootout after Emiliano Martinez made two saves.
"I will not be continuing as a coach as I was only doing this for a limited period of time, so this is my last game," he said. "What I'm leaving behind is an excellent group, personally and in terms of football, this is a very close team with a great spirit and a lot of skill. I was in charge for 20 games and we didn't lose in that time - that's for a reason."
"I'm really proud and I had a wonderful time. It is very painful to see how we have gone out after doing everything possible to stop it from happening," added Van Gaal. "It was a fantastic period of time, with the same group of players and I look back in a very positive way."
Looking back on the match, he admitted the Dutch had been below their best for a part of the game.
"In the first half, it was the same problem, we couldn't find a free player when we had the ball. I tried to change that at halftime, with a 4-3-3 and then a 4-4-1-1 and then a 4-4-2."
"We fought hard in the second half to try and get back from two goals down against Argentina, who pressed hard. We equalized, but we lost the shootout," commented Van Gaal.
"I have nothing to criticize the players. It's fantastic to come back from two goals down, but unfortunate to lose on penalties," he said.
"We ran much more than Argentina in the second half, but some players were really tired," said the coach, who explained his side had "worked on penalties ever since we got here and we were optimistic that we could win."