"The verdict which has been handed down overturning all convictions in relation to the Villagio Mall fire is very disappointing," Mr McCully said.
"The New Zealand Government understands the upset that families will be feeling and it is concerning that no one, so far, has been held to account for these tragic events.
"This case has been raised with the Qatar Government, including by the Prime Minister, in meetings earlier in the year."
Mr McCully said it was understood avenues of appeal were available and a civil case was underway. Officials at the NZ embassy in Abu Dhabi were making urgent inquiries about the next steps in the legal process, he said.
Martin and Jane Weekes, parents of the triplets, said the judge's decision was "devastating" news.
"The pain for all of the families is indescribable. Today we remember the 19 innocent lives lost, including 13 beautiful children. We are grieving for our beautiful children. And we are angry.
"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 needed to improve to become a forward-looking member of the international community.
The New Zealand Government had 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?" Mr Weekes asked.
"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."
None of the five people convicted -- including Gympanzee childcare co-owners, the Villagio mall's chairman and manager and a public servant -- will serve any jail time.
The Weekes' lawyer told them their best bet was an appeal in Qatar's highest court, the Court of Cassation.
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.
