Sinead was due to meet her mother and sister, Lauren Carr, the following day and are believed to have been informed of the news while in transit.
The family are now inquiring into why Ms McNamara was not taken to hospital immediately.
Mr Triantafyllopoulos, the family's lawyer, said in a statement: 'The family expects the Greek authorities to respond to the causes and circumstances of her death and incidents that occurred just prior.
'The deceased had telephoned her mother and brother shortly before the unfortunate incident under investigation.
'She was crying and referred to an incident that took place on the yacht with another crew member.
'The family state that Sinead was not having any problems, she often communicated with them and she was happy. In two days she will return to her family and her friends in Australia.
'The parents believe it crucial to thoroughly investigate both the events and incidents that preceded the death of their 20-year-old daughter died.
'In addition, they are looking for the reasons for the long delay between the time of the unfortunate incident and Sinead's transfer to an Athens hospital.
'She had been unconscious for several hours in a comatose condition and every minute was critical to her life.
'Expressing their trust in the Greek authorities, they hope that the critical issues above will be thoroughly explored and that they will receive appropriate answers for the sudden and unexpected death of their daughter.'