The Oranje put in a dramatic showing in the quarter final against Lionel Messi’s side, coming back from two goals down to equalise late in injury time.
However, they were outclassed in the penalty shoot-out with Argentina goalkeeper Emi Martinez making two excellent saves to deny Virgil van Dijk and Steven Berghuis.
Speaking after the game, van Gaal confirmed he would not continue in his role as coach.
He said: “First and foremost, I will not be continuing as a head coach for the Dutch team because I only did it for this period of time.
“This was my very last match. My third term as a head coach. In that time I coached 20 matches but I didn’t lose a single one. I think it is Google you can look that up on. I am looking back on a fantastic period of time with a great group of players.
“I don’t think I’ve been beaten today, only in a penalty shootout.
“I had a wonderful time and yes, it is incredibly painful to see how we have been eliminated. Particularly because I did everything to prevent this from happening.”
The 71-year-old manager will feel proud of taking the Netherlands to the quarterfinals of the World Cup after they failed to qualify at all in 2018. But he will leave his third spell as Holland’s boss disappointed after finishing second and third in 2010 and 2014. The Oranje remains one of the most successful footballing nations to never win a World Cup.