They had their chances but the women's Black Sticks weren't good enough to grab them as they lost their Olympic semifinal 3-0 to Britain today.
There is still the chance for a bronze medal, when they play world No 9 Germany on Saturday morning (NZT) but New Zealand were bitterly disappointed after being outplayed by a tough, determined British side, who are ranked three places lower than them.
Britain were helped by two penalty strokes early in the final quarter which took the steam out of New Zealand's challenge. In the final, they will play world No 1 the Netherlands, chasing a third straight Olympic women's gold, on Saturday. The Dutch beat Germany 4-3 in a dramatic penalty shootout after the scores were locked 1-1 at fulltime.
"We should have been more clinical," Black Sticks attacker Gemma Flynn admitted.
"We're very disappointed. We did try but didn't stick to our structures. We're hurting pretty bad. We've got to pick ourselves up. We've still got a bronze to play for.
"We have to put this to bed. We know what we've got to work on, keep our eyes up and chins up."
World No 4 New Zealand had plenty of scoring chances but could not find the finishing touch.
They looked the better team for chunks of the game and when attackers such as Sophie Cocks, Anita McLaren and Stacey Michelsen swept forward things looked promising.
However Britain, who beat New Zealand for the bronze medal in London four years ago, are nothing if not doughty. They had a toughness about them which counted at important stages.
Coach Mark Hager was left to bemoan a failure to stick to the game plan.
"I didn't think we played as a team," he said.
"We ran the ball too much individually and kept turning it over rather than play to our game plan, which was to play around the outside and get to the circle edges. But we played in the middle and to their strengths."
McLaren whizzed a penalty corner past the British goalkeeper Maddie Hinch's righthand post and New Zealand were able to lean hard on the British defence at times, but without breaking it.
Britain had their noses in front midway through the second quarter courtesy of sharp work by experienced attacker Alex Danson.When a penalty corner shot was blocked, she reacted sharper than the New Zealand defenders, diving in to nudge the ball past New Zealand goalkeeper Sally Rutherford.
The chances kept coming but frustratingly were not finished off.
The best opportunity fell to striker Olivia Merry. Unmarked on the left inside the British circle, she tried a first time shot which flew harmlessly wide when she had to to control the ball, steady herself and shoot.
Too often the ball would be crossed in through good leadup work only to roll behind, or beyond the reach of attackers in front of goal. As the chances evaporated Britain clearly grew in self belief.
Losing captain Kayla Whitelock for two periods hurt, the second coming when she was carded as Britain's first penalty stroke was awarded three minutes into the final quarter.
Helen Richardson-Walsh converted the chance, and Danson repeated that three minutes later when Liz Thompson upended Lily Owsley when she charged into the New Zealand circle from the left.
"We've got to be better as a team," Hager said. "Unfortunately we didn't have enough good players today. I've got to look at myself too, what did we do wrong tactically.
"I'm just gutted we didn't play as well as we can."
Four years ago New Zealand were really poor when playing for bronze, seemingly short on energy and commitment.
They can't afford that this time around. They played Germany in pool play, losing 2-1.
A win would give them the consolation of only New Zealand's second Olympic medal, to follow the men's gold in Montreal in 1976.
"We know what fourth place is like," McLaren said. "We've been in this position before and we know we're a good team.
"They have a chance to show it on Saturday.