"The decision was made in consultation with our vet who has over 20 years' experience caring for our animals, particularly cheetah,'' says chief executive Lynn Anderson.
"In our situation we have an absolute duty of care to provide the highest standards of welfare and to ensure a life worth living is provided to all animals we manage.
"Unfortunately the condition of the cubs was such that they were only being kept alive through 24 hour intensive veterinary care and could not otherwise survive.''
Zoo staff watched the births first unfold on CCTV, and think they may have seen Mazza eating two of her new babies.
They raced to the cheetah enclosure to rescue the three surviving cubs.
The surviving trio had initially responded well to being cared for around the clock in incubators at Christchurch's After Hours Veterinary Hospital.
But their fortunes have continued to fluctuate as zoo staff, and volunteers from the vet hospital, worked around the clock, bottle feeding them formula, and giving them immune-boosting blood top-ups taken from their absent mother.
"From the outset we had obvious concerns for these animals and we have since experienced many ups and downs in their condition,'' zoological manager, Rob Hall said.
"Overnight the cubs regressed further though and we were very worried that the animals had not significantly improved over the week.
"For example, by this stage (five days) the cubs should weigh around 700g but the biggest only weighs 589g. We made the right decision for the cubs; we could see that they weren't going to make it.''
The cubs have been sent for an urgent post mortem to ascertain the full cause of their problems.
"This documented case history now extends our knowledge of the species, not just for Orana but for the international breeding programme,'' Ms Anderson said.
"We have been overwhelmed by the level of support from the community and media surrounding the cubs and we sincerely thank everyone for their best wishes and interest.''
First time cheetah mothers often lose their litter due to inexperience.
It's not unusual for mothers to eat their young, or abandon them.
Mazza, 4, was also born at the park and she, along with her three brothers, was hand-raised by park staff when their mother rejected them.
Cheetah are a flagship conservation species for Orana Wildlife Park.
Only a small number of zoos worldwide have experienced repeated breeding success with the species.
To date, 18 cats have been raised to adulthood at Orana.