Netherlands started the competition brightly, winning all three group stage games against Ukraine, Austria and North Macedonia but failed at the first knockout round stage after losing 2-0 to Czech Republic.
De Boer replaced Ronald Koeman as Netherlands manager in September last year after the latter left to join Barcelona.
The 51-year-old announced his decision in an official statement on Tuesday, which read: "In anticipation of the evaluation, I have decided not to continue as national coach. The objective has not been achieved, that is clear.
"When I was approached to become national coach in 2020, I thought it was an honour and a challenge, but I was also aware of the pressure that would come upon me from the moment I was appointed.
"That pressure is only increasing now, and that is not a healthy situation for me, nor for the squad in the run-up to such an important match for Dutch football on its way to World Cup qualification.
"I want to thank everyone, of course, the fans and the players. My compliments also to the management who have created a real top sports climate here."
De Boer took charge of 15 games for Netherlands, winning eight.
De Boer has also taken charge of Ajax Amsterdam in the past, winning four Eredivisie titles in a six-year stint between 2010 and 2016.
He had ill-fated spells at Inter Milan and Crystal Palace after leaving Ajax as he lasted just 85 days in charge of the Italian giants and his time with the Premier League outfit lasted just four games into the 2017/2018 season.
