Younus Mahmood scored the winner for Iraq after 62 minutes in the under-23 tournament as Thailand have now lost in the bronze medal match four times.
They also finished fourth at the 1990, 1998 and 2002 tournaments.
But at least the Thais will get a bonus of around 14 million baht from private companies and the Football Association of Thailand (FAT).
"I am sorry for the Thai fans," said Thailand coach Kiatisak Senamuang.
"We wanted to return home with a medal and wrote a new chapter in our country’s footballing history but we failed."
“Congratulations to Iraq. Our players are disappointed but I told them they did a good job," he said.
"They proved that they could play at this level and against a good team like Iraq. They all have a bright future."
Kiatisak will take a break from football. However, he has said he would not coach the full national side for the Suzuki Cup (Southeast Asian championship) later this year.
At Incheon Football Stadium, Iraq were the better side in the first half and Mahmood came close to opening the scoring after just two minutes.
Thailand goalkeeper Kawin Thamsatchanan was one of the busiest players on the pitch as he was forced to make a couple of good saves.
Iraq, whose players were mainly from the squad that played at last year’s under-20 world championship, kept piling the pressure on Thailand but failed to score.
Thailand came back strongly in the second half and dominated for long periods in the opening stages.
But it was Iraq who went ahead when Ali Adnan’s corner found Mahmood who headed the ball home.
Thailand threw everything at Iraq in the final stages but failed to get an equaliser with striker Adisak Kraisorn and midfielder Charyl Chappuis denied by goalkeeper Mohammed Farhan.
"Iraq are a strong team and it is always difficult to play against them," said Kiatisak.
"At least we lost to a good team by only one goal."