The Antarctic Ocean Alliance said Russia's actions had left the commission "with nothing" after two years of work.
"All members, except Russia, came to this meeting to negotiate in good faith," alliance director Steve Campbell said.
During the negotiations, Russia, with support from Ukraine, had challenged whether the members had the legal right to set up MPAs in Antarctic waters.
Mr McCully said he had been open about the size of the challenge involved in reaching consensus.
"I am nevertheless deeply disappointed that an agreed MPA in the Ross Sea region has eluded us," Mr McCully said.
"Reports from the meeting make it clear that the vast majority of [commission] members have been flexible and constructive in seeking consensus.
"Reports also suggest that attempts to establish a consensus have been scuttled by the exercise of an effective veto."
Mr McCully said while there was room for reasonable differences about the relative positions of conservation, science and fisheries in any Ross Sea region MPA, it was undeniable that those differences should be resolved through constructive dialogue.
"This debate will not simply go away. International pressure for responsible leadership will intensify and New Zealand has every intention of playing its full part in ultimately achieving the right outcome."
The Green Party said it was disappointed at the outcome of the meeting and called on the Government to keep up the pressure to create a reserve.
"There is still hope for a Ross Sea MPA and we support the Government using all diplomatic avenues to make it happen," said oceans spokesman Gareth Hughes.
"While the outcome of these negotiations was disappointing, the process isn't over and there will be a new opportunity for negotiations in October."