"Not one person has taken responsibility for this crime. The charge has been reduced to corporate manslaughter. This is a travesty of justice," Mr Weekes said.
He said the Court of Appeal decision shows how far Qatar needs to improve to become a forward-looking member of the international community.
The New Zealand Government has to stand up and represent Kiwi interests to Qataris, he said.
"Their safety standards are third world. Their judicial system is not fit for purpose. It is one rule for Qataris and another rule for all others.
"It is an unsafe place to live, work and visit...they cannot even guarantee public safety with basic protections. How can anything go ahead in these circumstances?"
Prime Minister John Key met with the Emir of Qatar when he visited the country earlier this year over the tragedy, his office said today.
He told media at the time that Sheikh Tamim bin Hamad Al Thani had "assured" him he was committed to seeing justice for the Weekes family.
But Mr Weekes said it was not the case.
"This isn't the justice we were hoping for," he said.
"Now is the time for the international community and especially New Zealand to remind the Qatari government of their responsibilities to our family and the other families effected, for justice to be done."
Mr Key was overseas and unable to comment on the decision today.
None of the five people convicted - including Gympanzee childcare co-owners, Villagio mall chairman and manager and a public servant - will serve any jail time over the devastating fire.
The Weekes' lawyer told them their best bet was an appeal in Qatar's highest court, the Court of Cassation.
"Our local lawyer has told us: For the nursery and Villagio the judgement made many mistakes in facts and law and make it to appear no justice has been applied and you hope that the attorney general will appeal it with the Cassation Court' [sic]."
Some family members stormed out of the court after the ruling was delivered, Doha News reported.
In the Court of Appeal ruling, judge Abdalrahman al-Sharafi said he was throwing out all the testimony from family members that led to a guilty verdict, arguing they could not be witnesses and plaintiffs in the same case.
He found the company that owns the shopping centre guilty of manslaughter - meaning the only avenue left for families is to seek financial compensation.
The company was also ordered to pay a fine of QR $20,000 (NZ$8000), the maximum penalty under Qatari law.
Doha News reporter Peter Kovessy interviewed families outside court - many of whom were shocked or disgusted, he said.
He told Radio NZ one of the central issues of the case was whether the childcare centre was a "nursery" or a "children's entertainment area" - because of the difference in regulations.
"Ultimately [the judge] ruled in favour of the arguments put forward by the defence attorneys that this was indeed a children's entertainment area and that effectively tossed out a lot of the charges of negligence that led to the original conviction."
A memorial page set up for the Weekes triplets said the news was "absolutely heart-breaking".
A post on the Facebook page - coordinated by mother Jane Weekes' triplet support group - about the decision has been shared more than 130 times already this morning.
Friends of the family have commented messages of shock and support on the post, saying it is "utterly unbelievable".
Facebook user Kerry Mack said people in Doha would never forget the triplets.
"How is this possible??? And shame on the judge to stoop so low as to try and place blame on the deceased gympanzee staff...There are many of us in Doha who will never forget your children," she wrote.
Hayley Kinley wrote: "Your 3 little monkeys, their friends and teachers have been forgotten along the way by those who have the power to punish those responsible. But we will never forget. Wishing you much strength in the days ahead xxx."
Liz Lee wrote: "It goes on and on, so much loss and heartache and still no accountability. We are heartbroken for you all."
