John Volanthen, one of the two British divers who found the boys, played down the gallantry.
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Two other British cave divers who assisted in the mission were John Volanthen and Jason Mallinson.
The Thai Navy Seal unit orchestrating the mission confirmed on its Facebook page that the remaining children, said to be the weakest of the group, had been guided out of the tunnel network.
The team and coach had ventured into the complex after a practice but became trapped when heavy rains flooded the way they'd come in.
Prayuth Jetiyanukarn, abbot at Phrathat Doi Wao temple, where the coach worked, said the coach had a strong bond with his Wild Boars football team and would have kept them "calm and relaxed" inside the cave.
The Thai Navy Seals also released video showing the three-day effort to free the boys.
Volanthen and fellow Brit Rick Stanton were the first rescuers to find the boys deep in the Tham Luang cave complex.
He added: "We are not heroes".More news: PGA: 3M Open Set For Fourth Of July Week In 2019
All 12 of the boys and their 25-year-old coach were brought to safety over the course of a three-day rescue, organised by Thai Navy SEALs and an worldwide team of diving and caving experts, that ended on Tuesday.
"They had already been doing the most extraordinary dives through the cave and laying the very robust rope which made all subsequent dives to the soccer team not only possible, but safe", he wrote.
Banphot Konkum, father of Duangpetch Promthep, shows a picture of his son during an interview in Mae Sai district in Chiang Rai province, northern Thailand, Friday, July 13, 2018.
The boys now recuperating and the rescuers who brought them to safety are starting to share stories of the dangers and their survival. And only a day later, a second movie was announced - but this one promising to circumvent that dreaded Hollywood tendency: whitewashing.
They were found 10 days later, huddled on a small, dry shelf just above the water, and divers and other global rescuers plotted the complex mission to rescue the team before more rain came.
"I think Dr. Harry, the Australian doctor, he's very good", Volanthen said.
"The favourable outcome that has been achieved is nearly beyond our imagination when we first became involved in this operation", they said. "So, that seemed to work".
He thanked the pairs' families for dealing with the media and the "worry we caused them" as well as sending "heartfelt condolences" to the family of former Thai Navy SEAL Saman Gunan who died during the rescue efforts. "It's kind of bittersweet for what's otherwise been an excellent operation".