"Duncan loved snorkelling and accepted the dangers he may face in the ocean. He was extemely unlucky this time," the statement said.
New Zealand's Ministry of Foreign Affairs and Trade confirmed it had not been contacted in relation to Craw's death.
"The Ministry of Foreign Affairs and Trade has not been approached by the family of Duncan Craw for consular assistance," a MFAT spokeswoman said.
Craw was married and had a young son named Levi.
South Australian police inspector Campbell Hill told local media outlets emergency teams were called to the scene about 5pm last Thursday.
"We were called to a reef break just out of Port MacDonnell where we were met there by the family," Hill told reporters.
"The man could not be located and a large-scale search commenced involving police officers, water operations members and the air wing, local state emergency services and fisheries.
"There were also a lot of locals helping with the search, standing upon paddleboards and fishing boats, or standing at shore with binoculars."
A police helicopter spotted a Great White Shark in the area later that evening.
The next morning search teams found a badly damaged wetsuit along with other equipment understood to have been used by Craw.
"Unfortunately we have put it all together and it certainly paints a picture of a fatal shark attack," Hill said.
Craw went missing just three days before his 33rd birthday.
He was described as an extremely hardworking and dedicated operations manager at an agricultural company in Warrnambool, where he grew up after moving from New Zealand at a young age.
"When he wasn't farming, spending time with the family, or working around the property he bought with his wife Taylia, he liked catching up with friends and watching or playing sport, including cricket for Woolsthorpe Cricket Club," his family said.
"He was also the best father to Levi and a beautiful husband and best friend to Tay, his high-school sweetheart."
"He was a cheerful, loving, helpful son. He was a kind and cheeky brother to his sisters. He was a fun-loving, mischievous and supportive mate who had a heart of gold."
Craw's death comes as eight Australians were killed by sharks last year - the most since 1929.
It also comes as 19-year-old Kaelah Marlow died at Bowentown Beach in the Bay of Plenty in New Zealand earlier this month.