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After a draw against Argentina and loss to the Netherlands, GB needed a win to retain realistic gold medal prospects but conceded within the first minute.
Stacey Michelsen capitalised on slack defending before defender Crista Cullen left on crutches with a leg injury.
"We're gutted about the result," forward Sophie Bray told BBC Sport.
"We created the chances and just couldn't put them away, but ultimately you probably learn more from a loss."
Having faced the two strongest teams in the tournament already in Argentina and Netherlands, GB were hoping to secure their first win at the 2016 Champions Trophy campaign against the world number four side.
However, despite the best efforts of Bray, Lily Owsley and Susannah Townsend, GB could not find a way past New Zealand keeper Kayla Whitelock.
Britain need to win their remaining two matches and hope for an unlikely sequence of results between the other five nations to go in their favour in order to reach Sunday's gold medal final.
A more realistic aim is the bronze medal match, which would be achieved by defeating both USA on Thursday and Australia on Saturday.
GB head coach Danny Kerry told BBC Sport: "I actually thought we played well for three quarters today and they need to be tournament resilient and not be too down."
Kerry said it was "too early to say" how serious Cullen's injury is, but with the Olympic team due to be revealed in just a week's time, it will be a concern.

Jarvis, 29, has won 17 caps for Wales and last played in the Six Nations win over Italy in March 2016.
James, who will miss the first match of the three-Test series against the world champions in Auckland, has not recovered as quickly as hoped, but remains with the squad.
Wales have lost 26 matches against the All Blacks since beating them in 1953.
James is also likely to miss the game against the Chiefs in Hamilton on Tuesday, 14 June.
Jarvis, who is joining French Top 14 side Clermont Auvergne from Ospreys, will arrive on Wednesday morning in New Zealand.
The Exeter-born player graduated to professional rugby via the Bath academy, and played for England Under-16s and U19s.
But he successfully pursued Wales honours via Ospreys, having been eligible because of his Merthyr Tydfil-born grandmother.
He has started six Wales games, coming off the bench for the remainder of his caps.
Britain's hopes of a first women's Champions Trophy title look over after a disappointing 1-0 defeat by New Zealand in London.
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Tight-head prop Aaron Jarvis is flying to New Zealand to join Wales as cover for Paul James, who has a calf injury.