A majority of 56 percent voted against independence from France but the Caledonian Union said the result confirmed that the struggle for independence is legitimate.
Polls predicted a much larger winning margin.
In a statement to its supporters, the party said 2019 would be important to prepare the next independence referendum due to be held next year.
It said the party wanted an open society and a better redistribution of the wealth which had been seized more than a century ago.
In a separate message, the FLNKS umbrella group called for a new societal model which included all sides to work together to ensure a fair distribution of the wealth being created.
It also called on young generations to assume their responsibility to build a new society.