Volanthen is understood to have returned home to Bristol.
Her words are likely to give comfort to the 12 boys who were last seen in a recent video that showed them recovering in isolation at the Chiang Rai Prachanukroh hospital after more than two weeks underground.
All of members of the team were successfully rescued from the cave on Tuesday after being trapped there for 18 days.
The British divers who blazed the trail were praised by Australian doctor-diver Richard Harris, who stayed in the cave for three days to oversee the medical care of the boys while they were waiting to be rescued.
Citing an update from hospital director Dr Chaiwet Thanapaisan, Thongchai said the youths' relatives were allowed to visit them on the condition that they wear a face mask and wash their hands before and after visiting.
During the mission to save the boys, a former Thai Navy SEAL Saman Kunam died after volunteering to lend his expertise.
"Meanwhile on the ground, the Thais and worldwide community sent in swarms of men and women to provide everything from catering, communications, media and of course the huge teams of workers filling the cave with tonnes and tonnes of equipment to try and lower the water and sustain the diving operations", Dr Harris wrote.
"I have never seen anything like it with man battling to control the natural forces of the monsoon waters".
The last group of the 12-member "Wild Boars" soccer team and their coach was brought out of the Tham Luang cave, near the border with Myanmar, on Tuesday night, safely ending a unsafe rescue and evoking global relief and joy.
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They expected to be in the cave for only an hour when high water was suddenly upon them.
The Tourism Authority of Thailand (TAT) said last week, after the team had been found alive, that it planned to promote the Tham Luang cave complex in the province of Chiang Rai as a tourism attraction as it had featured so heavily in news stories around the world.
At the first training session since their teammates went missing in a Thai cave, the remaining "Wild Boars" said they can not wait to see their friends back on the pitch. It was very cold at night and pitch dark.
The team became captured within a cave in Thailand on June 23 and survived for 18 long days before being miraculously rescued by a courageous group of global divers.
John Volanthen said he's just relieved the boys are all alive, and praised the collective effort of the global contingent of rescuers.
"I want to tell the boys, please don't blame yourselves", Valeepoan Kunan said, as reported by Reuters.
Dr Harris and Dr Challen spoke out about the gruelling rescue mission for the first time on Thursday, sending a message of thanks for the support they had received.
Mr Volanthen's mother, Jill, said: "We are absolutely so proud, but my sympathy is with the wife and family of the diver who lost his life".