The Tartan Army failed in their mission to make it through the group stages of a major competition for the first time in their history as they finished Group C in third place.
Three points, and crucially a goal difference of -3, was not enough to see them progress as one of the best third-place sides at the tournament after a stack of results went against them as the Round of 32 knockouts were confirmed.
Clarke waited for mathematical confirmation of Scotland's exit before issuing his statement despite signing a contract extension until 2030 prior to the World Cup.
"The most emotional part of this goodbye is for my players, without whom we wouldn't have had any of the memories we've accumulated from 2019 until now.
"They deserve all the praise and adulation they receive and it was truly an honour to be called their gaffer. Thanks for having me and good luck to my successor."
Clarke moves on as Scotland's longest-serving national team boss after leading the team to three major tournaments including back-to-back UEFA European Championships.
The next question now focuses on who will replace him at Hampden Park with Everton's David Moyes the early frontrunner as he enters the final year of his contract on Merseyside.
Moyes has previously been linked with a move to take charge of his country, either side of returning to Everton back in 2025, but the timelines need to match up.
Scotland start their Nations League campaign in September with Euro 2028 qualifying from March 2027 and Clarke's former assistant Steven Naismith - who played under Moyes in his first spell at Everton - could take interim charge until a decision is made on a permanent successor.