The Netherlands had been tipped to make a run deep into the tournament, but Morocco beat them 3-2 in a penalty shootout after the match in Monterrey on Monday finished 1-1 at the end of extra time.
The Dutch were leading 1–0 in the final minutes of an enthralling match thanks to a Cody Gakpo goal, but they conceded an equalizer deep in stoppage time when Issa Diop scored.
Justin Kluivert, Quinten Timber and Crysencio Summerville all missed their efforts in the shootout.
“Last night I took the decision to end my stint as head coach of the Dutch National Team,” Koeman, 63, said in a statement on Instagram.
“We all shared the dream of making history at this World Cup, but we fell short. No one is more disappointed by that than I am.
“As head coach, the responsibility ultimately rests with me.”
Koeman alluded to the health struggles of his wife Bartina, who has been diagnosed with breast cancer.
“The past years have made me realise again that there are more important things than football,” he said in his statement.
“Football has been my life, but health is priceless. When someone you love is fighting a tough battle, your perspective changes.”
The former Barcelona player and coach, who has had stints in charge of English clubs Southampton and Everton, was in his second period in charge of the Netherlands.
Meanwhile, Dutch football chiefs condemned online racist abuse aimed at Netherlands players following their elimination from the tournament.
The Dutch football association said: “Football brings people together, regardless of origin or background.
“We have seen online reactions in which players have been subjected to racist and discriminatory abuse following the team’s elimination.
“We draw a clear line against such behaviour. Racism and discrimination have no place in football, online, or in our society.”
