The 46-year-old woman, who identified herself only as Kay, spoke to Croatian news outlet HRT shortly after arriving back on land.
Her father, Ron Longstaff, told the Press Association he was still trying to establish what had happened, as conflicting reports emerged of how the British woman ended up in the water. "These wonderful guys rescued me".
The Croatian rescue ship sent out to look for her found her just 1,300 meters from where she fell. Within a few minutes, a coast guard swimmer, Lt. Marina Delic, got her to safety.
MailOnline quoted Irena Hrstić, a spokeswoman for the hospital, as saying Longstaff was being "assessed for stress" but is "physically fine".
The circumstances of the incident were being investigated.
In this photo taken August 19, 2018, a woman who identified herself as Kay from England, center, is escorted by rescuers from a Croatian Coast Guard vessel in the port in Pula, Croatia.
Lovro Orešković, captain of the Cavtat, said: "We have saved a human life, and nothing else compares to it. I was sitting in the sun with her a few weeks ago".
Miss Longstaff worked for Virgin Atlantic before joining a number of private airlines, and has lived in Hove, East Sussex, and Cheltenham, Gloucs. Although, the Daily Mail reports that Kay may have had a row with her boyfriend before the incident, leading to speculation that she may have purposely jumped from the ship.
It's not easy to survive after going overboard a large cruise ship.
The drama unfolded as the Norwegian Star was heading back to Venice after a seven-night east Mediterranean voyage, taking in Kotor, Montenegro and the Greek islands.
University of Portsmouth professor Mike Tipton told BBC News that Longstaff fell into a "perfect" survival situation since the water was warm and calm. "She told us she does yoga, and that as she floated in the sea she sang the whole time so that her body temperature wouldn't fall, and to stay awake". "I'm lucky to be alive", she added.
The Croatian Ministry of Maritime Affairs spokesman David Radas told the newspaper, "Our rescuers were in touch with the Norwegian Star's crew and by checking CCTV knew the exact moment she fell in the water".
A passenger said holidaymakers booked on the ship's next voyage were to be compensated as the delay caused by the search for Ms Longstaff meant they would miss a stop at Kotor in Montenegro.
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