The Dorchester fighter lost 10-8 to an opponent from the host nation in his opening -80kg bout in the 2014 Gyeongju Korea Open International Taekwondo Championships in South Korea, informed the DorsetECHO.com.
Cook, competing for the Isle of Man, heads the world and Olympic rankings and is still on course to represent Great Britain at Rio 2016.
The 2014 Gyeongju Korea Open International Taekwondo Championships opened in the South Korean city of Gyeongju on July 11, and will wrap up on July 16.
The competitions are being staged in junior, senior and cadet categories. Cadet competitions are being held in two sections: 8-10 and 11-13 years old.
A total of 1,770 athletes are taking part in the five-day international taekwondo tournament.