The team's combined results earned them a ranking of 17th overall among the 38 nations entered, the Kiwi trio finishing just one point shy of 16th.
Team manager Bevan Weal, from Taupo, said he was "extremely proud" of his riders.
"Cody (Cooper) was like a rock, with a very solid performance coming from the veteran. He can again rate himself among the top riders in the world and that's very impressive for a rider aged 32," said Weal.
"Hamish (Harwood) had a difficult start to the weekend and was forced to nurse an injured shoulder throughout Sunday's races. He tenaciously gritted his teeth and braved the pain and did his country proud.
"For Josiah (Natzke), it was his first time at the MXoN. I know he has been racing GP events this season, but he really stepped up this weekend. This was another level.
"Bring it on next year I say."
Team France won the event overall, the third consecutive time they have won the MXoN, but it was tight and came down to the final race of the weekend, with the Netherlands and the United States of America also potential winners.
With Dutchman Jeffery Herlings taking an early lead, the crucial third and final race of the 2016 MXoN was mostly an exciting battle between US rider Cooper Webb and another Dutchman, Glen Coldenhoff, then Webb battling with French rider Romain Febvre.
Webb had a slow-speed crash late in the race, and with team-mate Jason Anderson sidelined with injury, the places he lost meant Team USA dropped back to finish the weekend third overall.
An 11th placing from French rider Gautier Paulin in that final race was enough to tip the scales in France's favour, with the Netherlands finishing runner-up and Team USA third.