With Norway thrashing the Philippines 6-0 in the other Group A game, the Football Ferns needed to beat its Swiss opponents to secure a place in the last 16 but was unable to find a breakthrough.
In front of an excited crowd at the Dunedin Stadium, New Zealand struggled to get to grips with a cagey match and failed to create many chances on goal.
The results on Sunday mean Switzerland go through as the group winners, with Norway progressing as the runner-up ahead of New Zealand on goal difference.
The tournament had started so well for the cohost when it shocked Norway 1-0 in the opening game, securing its first ever World Cup win.
But all the excitement that was generated from that famous victory slowly faded over the remaining group matches.
The Football Ferns were stunned 1-0 by the Philippines in their next fixture and then struggled to stamp their authority over Switzerland when the pressure was on.
New Zealand only managed two shots of target during Sunday’s match despite throwing everything at its opponents in the closing stages.
In search of the winner, New Zealand goalkeeper Victoria Esson joined the attack whenever her team had a corner or freekick in the final minutes – she even managed to get her head to a cross but couldn’t direct it towards goal.
After the defeat, New Zealand’s players huddled on the pitch and captain Ali Riley gave a speech to her tearful teammates.
New Zealand’s misery meant jubilation for a Norwegian team that recovered from defeat in its opening game to qualify for the knockout rounds.
The 6-0 win against the Philippines was a welcome return to form, finally showing the team’s potential to go deep into the tournament.
Norway’s Sophie Román Haug scored the second hattrick of the tournament, with Caroline Graham Hansen, Guro Reiten and an Alicia Barker own-goal completing the rout.
The Philippines’ Sarina Bolden, who scored the team’s historic first World Cup goal in their win against New Zealand, said Sunday’s loss “burns right now” but that the team is looking ahead to building on the experience.
“I’m just happy that we made it to the World Cup and happy that we were able to get a result, get a win,” she told CNN Sport.
“Not many teams have been able to do that, especially debutantes. Even though this part of our journey has finished, it’s taught us so much and next steps is just to keep getting better.”
The crowd at Eden Park could be heard chanting ‘Filipinas’ throughout the game against Norway, a sound Bolden won’t forget in a hurry.
“It felt like a home game, which doesn’t happen often especially in the World Cup,” she added.
“It just shows that Filipino supporters are truly everywhere. We wouldn’t have made it this far without them.”