The other occupants got out of the vehicle and a man grabbed Emily's mother, Sandra, but lost his grip on Emily because of the strong current.
Emily's parents, Michael and Sandra Saunders, have spoken of their daughter as "a happy, cheeky little girl".
They released a family statement through police on Saturday thanking everyone involved in the Poerua River search effort.
The couple also paid tribute to Mr Petrie, who died trying to save their daughter.
"We would like to thank the police, search and rescue and all the countless people involved in the ongoing search for Emily.
"We would also like to thank the local community for their kind help and support during this difficult time.
"Our thoughts are with Barry's family as well at this time. His efforts trying to save Emily will never be forgotten.
"Our daughter, Emily, was a happy, cheeky little girl who loved the outdoors."
NZME, on the weekend, uncovered the dramatic details of the frantic efforts to save the toddler and her mother as they were swept out of their vehicle.
Mr Petrie was out possum trapping with several others near the Poerua River, south of Hokitika, just after midday on Thursday. The group were picked up by Michael and Sandra Saunders who were travelling with their daughter, Emily.
As they tried to cross the river, the Saunders' 4WD got stuck and became submerged.
Frank Simpson, who owns the farm where the Saunders work as sharemilkers, revealed what happened in the terrifying moments that followed.
"They had to abandon the vehicle and that's when it all happened," Mr Simpson told the Weekend Herald.
"One of the guys grabbed the little girl and Sandra at the same time, but he lost his grip on the little girl because the river was running that fast, he was up to his chest in water."
