Mrs Purdy told Wales Online that Jack "is mildly autistic and had a stomach migraine where he was vomiting violently."
"He started feeling ill and to be fair to the hotel staff they let him lie down and keep cool. We arrived at the airport and I had booked a VIP lounge so we were able to go there.
"My son was still ill and the staff decided to call a doctor, despite me telling them that when he gets like this, nothing can be done for him".
"But the doctor came and took him, and his boarding pass and said they would put him on the flight in priority seating."
"I noticed he was not in his allocated seat, but we were right at the back. I thought he was sat further down the front, there was no reason he would not be on that flight."
It was not until they were collecting their luggage at the airport in Cardiff that the family realised Jack's bags were missing and his mother could not find him.
They searched for three hours with the help of the police, airport security and the British Consulate until they discovered Jack never boarded the plane.
He was stuck in Crete without his passport, mobile or money.
"It would have been awful for this to happen to someone more vulnerable or younger than Jack. I thought he was safe and was on the flight. It had never happened to me before. Why would I not assume he was on the flight?" Jack's mother told Wales Online.
After some time, Jack returned home accompanied by a TUI manager.
"He was tearful. When he got home he was still not well at all," Jack's mother added.
"It's awful what has happened to my son. I felt completely out of control of the situation. It was such an awful experience."
"I am livid, this caused so much distress to all of us, especially my youngest children, who were inconsolable."
Mrs Purdy believes that "TUI should compensate us and ensure it does not happen to anybody else."
A TUI UK spokesman also told Wales Online that "we are sorry to hear that Mrs Purdy's son was taken ill in the airport lounge before his flight."
"Once we were made aware that he had returned from hospital and was still at the airport we fully supported them by arranging both a flight back to the UK and onward travel home, covering the entire cost.
"We were in direct contact with Mrs Purdy to keep her updated with the situation and have tried to make further contact following their return to the UK."