Japanese official Emi Yamada ruled that a firm reverse stick shot by star Argentina attacker Carla Rebecchi had come off the back of her stick. She whistled when the ball was in mid-air.
The replay showed it was a fair goal but New Zealand could complain the initial decision should have stood.
Both teams had 16 shots on goal, Argentina edged the circle penetrations 24-23 and had 55 percent of possession while fourth-ranked New Zealand had three penalty corners to two.
However Argentina took their opportunities better, some of New Zealand's defensive play bringing the ball out from their defensive circle was poor and Argentina had the most effective players on the park in Rebecchi and Maria Granatto.
The early signs were encouraging, both Petrea Webster and Charlotte Harrison got shots in on goal, and Argentina's opener had a touch of luck about it. Florencia Habif's shot from Argentina's first penalty corner deflected off a New Zealand stick past goalkeeper Sally Rutherford.
However Rutherford was at fault with the second eight minutes before halftime. Her block off a ball driven in from the right was totally ineffective and rolled the ball straight to Rebecchi in front of goal, who doubled the lead.
Argentina were starting to take a grip on the game and when Rebecchi's second goal came two minutes after the restart, things looked grim.
To their credit, New Zealand smartened up, showed greater urgency and were rewarded through a good goal by Sophie Cocks, swivelling under pressure to send a firm shot into the Argentine goal.
She thought she had a second goal, with a neat deflection, only for Argentina to successfully refer the incident, which showed the ball had subsequently deflected off Cocks' shin.
Granatto was always a handful for New Zealand's defence and her cracking individual goal, beating a couple of defenders before thumping a shot past replacement goalkeeper Amelia Gibson's left hand, sealed the win.
There was a late consolation goal for Olivia Merry after an out-of-sorts Anita McLaren and Kelsey Smith had set it up four minutes from the end.
But there could be no complaints at the outcome. New Zealand might also be fretting over a leg injury to key defender Liz Thompson in the first half.
''We were just poor with our basic skills today," Hager said. ''We need a few more players stepping up in tough times. Whether it's Olympic selection nerves I don't know but at the moment we've got two or three players playing well."
New Zealand need to beat the seventh-ranked United States in their final round robin game on Sunday morning to have a chance of playing for third place.
