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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.
Britain's hopes of a first women's Champions Trophy title look over after a disappointing 1-0 defeat by New Zealand in London.