Great Britain eventually scored in the 64th minute through a Stephanie Houghton long-range free-kick that sliced through the New Zealand wall and caught goalkeeper Jenny Bindon out of position.
New Zealand had lofty ambitions at the Olympics - they still do - but they knew this was a missed opportunity. With competition in every other sport yet to start, they had the chance to grab some attention and momentum.
"The players are devastated in there," coach Tony Readings said. "But we have shown it time and time again that when we get these [sorts of] defeats, it just sparks new life into the players and they are even more determined."
There will be few more determined than Gregorious. She looked crestfallen when she butchered her chance in the 72nd minute and the enormity of the miss hit her at the final whistle as the tears flowed.
"It's probably going to haunt me for the next little while but I have to put it behind me and move on to the next one," she said. "Hopefully it will be quickly forgotten and I will put a few away the next time I get them.
"I don't think anyone was more surprised than me [to get the chance]. You dream of those sorts of opportunities and it was a defender's nightmare. I felt a bit like a kid on Christmas ... and then you saw the result of that."
New Zealand can still make the quarter-finals in a generous competition of only 12 teams but will need to be much better. They play Brazil, the world's fifth-ranked side, in Cardiff on Sunday morning (NZT) before a winnable game against Cameroon - Brazil beat Cameroon 5-0 in the late game.
Great Britain are a good side (England are ranked ninth) but it was the manner of the defeat that disappointed the most.
The Football Ferns felt ready to make a statement on the world stage after some good results this year - they were unbeaten in nine games and threatened to beat world No 1 USA until conceding two goals in the last five minutes - and believe they are the equal of any other side.
"We expect to win these games," Readings said. "That's how far this team has come."
Instead, once Great Britain calmed down after 15 minutes and pressed higher up the pitch, New Zealand looked panicky and gave away possession far too easily. Only some scrambling defence, handy goalkeeping nd the woodwork kept Great Britain scoreless.
They finished strongly after Houghton's well-struck goal but the damage had been done.
"What the players will know today was that it was a missed opportunity," Readings said.
"We know we could have and probably should have taken something out of the game. We will be going into the next game against Brazil and there will be some unfinished business from us."
Great Britain (Stephanie Houghton 63) New Zealand 0. And: 0-0.
