Malaysian Police said there was no suspicion Nora was the victim of foul play.
Nora's family remain skeptical there weren't more factors at play that led to her eventual death from an intestinal rupture caused by starvation.
Her unclothed body was discovered on Tuesday in a ravine in dense jungle following a 10-day hunt involving hundreds of people, helicopters and sniffer dogs.
But the girl's parents, who initially believed she might have been abducted after they found her missing from their resort on the morning of August 4, said they are "still struggling to understand the events of the last 10 days".
According to the statement, the family also thanked the Malaysian authorities for their ongoing support and cooperation with global governments and police as criminal and missing persons investigations continue.
"Nóra is at the heart of our family", they said.
The family said this in conveying their gratitude to all those who where there to help during the family's hour of need through a statement issued by the Lucie Blackman Trust, a British charity which supports its nationals in times of crises overseas.
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"We know why Nora died, in simple terms from starvation, we know where she ended up, but we don't necessarily know how she got there".
But they said their daughter "died in extremely complex circumstances" and they were still hoping to have "more answers to our many questions".
Mr Morel said the family was also keen to obtain toxicology results that may shed some more light on Nora's disappearance. "The cruelty of her being taken away is unbearable".
Search teams and local volunteers scoured the area around the resort for days before finding Quoirin's body.
"We will be bringing Nora home where she will finally be laid to rest, close to her loving families in France and Ireland", they said.
A window was found open downstairs in the holiday cottage where she was staying. She was estimated to have been dead two or three days when her body was found.
An initial investigation revealed no evidence of criminal behavior but police would look at all possibilities, Malaysia's deputy police chief Mazlan Mansor has said.