Asked how much credit should be given to the conservation group Sea Shepherd, Mr McCully said: "We have to be careful about having a counter-productive effect on these developments.
"There is a big chunk of what Japan has been doing that is motivated by Japanese pride. Anything that plays into that process could be counter-productive.
Read more: Environment blogger Sam Judd says the court decision is a momentous win for whales.
"There are warehouses of whale meat in Japan. There has been no good science conducted. It has been a practice that has continued partly because of Japanese pride.
"And I think we should just give them some space to get past that... and having international NGOs and governments ramming this judgement in their face is not going to help this process."
Watch: McCully's warning after whaling ruling
Mr McCully said he hoped that Japan would realise that it was "game over".
It was possible that Japan could put in a new proposal for a scientific whaling programme in the Southern Ocean which met the terms that the courts had outlined.
They could also move to other territories such as the northern Pacific.
But he said it was important to give the Japanese Government time to consider the judgement and to continue diplomatic discussions.
"I just don't want to encourage anything that is going to cause the Japanese Government to think about a new programme."
He was optimistic that the judgement's definitions of scientific purposes would make it difficult for Japan or other countries to develop another programme.
Prime Minister John Key told 3News that with 16 judges on the panel at the International Court of Justice, the decision was "very comprehensive".
"I think it's more comprehensive than probably even we had hoped it would be."
A 'damning verdict'
International Fund for Animal Welfare's Oceania branch spokesman Matt Collis told Radio New Zealand it was a "pretty damning verdict".
Watch: Japan to end whale hunt
But despite the clarity of the judgement, it was unclear what Japan's next move would be.
It was unlikely they would leave the IWC, because there would be a "significant political cost" to doing that, Mr Collis said.
While there was some room in the judgement for scientific whaling, there were a lot of details in the ruling on what would meet that criteria.
"I think in practice it's going to be very hard for Japan to deliver something like that."
Labour Party's Foreign Affairs spokesman David Shearer said the result was a vindication of the Australian and New Zealand decision to give evidence at the court.
A minke whale is unloaded at a port after a whaling for scientific purposes in Kushiro. Photo / AP
"Like New Zealand, Japan has always placed great importance on the international legal order and the rule of law. Japan's early statements that it will abide by the ICJ's ruling are welcome."
Diplomatic efforts were now needed to ensure that new loopholes were not found to continue whaling operations, Mr Shearer said.
Greenpeace campaigner Karli Thomas said the ruling vindicated its view that whaling in the South Ocean was not necessary for science and should be ended.
"We urge Japan to abide by this decision, scrap the factory ship Nisshin Maru and not attempt to continue whaling by amending the program and claiming it is now scientific."
The Greens' Gareth Hughes said it was always obvious 'scientific' whaling was simply a guise for commercial whaling and now the International Court's ruling made that clear.
"While Japan says they will abide by the ruling diplomatic pressure needs to be continued by the New Zealand Government to ensure Japan don't seek to use a loophole."
Sea Shepherd Australia chairman Bob Brown said the finding vindicated "a decade of courageous actions by Captain Paul Watson and his crews".
"All across Australia people will be celebrating this win due to Sea Shepherd and their huge public support for protecting whales in this country that led to the Australian Government to take this legal action."
Earthrace Conservation founder Pete Bethune, who was at the court for the original case said: "I am absolutely thrilled. Today will go down in history as a great day for whales, for conservation and for justice."
ICJ ruling
Delivering its judgment on Australia's case against Japan, which saw evidence presented during a three-week hearing last year, the ICJ found Japan's whaling programme in the Antarctic failed to meet the conditions for scientific whaling under regulations set by the International Whaling Commission (IWC), the body charged with the conservation of whales and the regulation of whaling.
It was ruled that no further permits for scientific whaling should be issued under Japan's scientific whaling programme.
In a 12-4 majority judgment, the UN court sided with Australia, finding that Japan's program fell short of following scientific methods, the Associated Press reported.
"The court concludes that the special permits granted by Japan for the killing, taking, and treating of whales ... are not 'for purposes of scientific research'," presiding judge Peter Tomka said.
Attorney-General Chris Finlayson gave evidence on behalf of New Zealand during the court case in the Hague July last year.
He told the court that Japan was wrongly interpreting article eight of the whaling convention, which deals with scientific permit whaling.
"Under Japan's interpretation ... the convention is solely a vehicle for the optimum utilisation of whales through commercial whaling - nothing more than an industry cartel," he said.
Mr McCully said today that the court had ordered Japan to cease whaling under one program but he warned it could try to put together a new program that would meet some of the tests the court had outlined.
"We hope that won't happen and in the short term it won't because this is going to take a bit of working through," Mr McCully told National Radio.
"This judgement ... is very firm and very clear but it still does leave Japan with a decision to make after they've digested this, which is to look at whether they try to devise a new programme that is scientifically based that embark upon whaling in the Southern Ocean again. Our task is to make sure that we carry out a diplomatic conversation that dissuades them from embarking on that course."
