New Zealand had the high of a win in their opening game, but were eliminated on Sunday with a draw against Switzerland.Credit…Lars Baron/Getty Images

The story of New Zealand’s journey in the Women’s World Cup, and of its exit on Sunday night, will be a familiar one to the team and its fans: not enough goals for New Zealand, and too many for everyone else.

For New Zealand, a co-host of the tournament with Australia, the ride had begun on a high. The team had earned its first-ever World Cup victory in the event’s opening match, leading a rugby-mad country to stir, if only momentarily, for women’s soccer. For a few days, even bigger achievements seemed possible.

But the opening victory had been narrow — the Football Ferns, as the team is known, had scored a single goal — and perhaps that was a sign. New Zealand never scores much, and it never scored again at the World Cup, eliminated quietly on Sunday in Dunedin after a 0-0 tie with Switzerland that was the home team’s ninth goalless outing in 12 games this year.

“Obviously we talked and we were proud of ourselves and what we’ve been able to accomplish, but at the end of the day we wanted to get out of this group stage and we just didn’t,” New Zealand midfielder Malia Steinmetz said. “It’s just black and white.”

In Auckland, meanwhile, Norway was raining goals on the Philippines, winning by 6-0 to save what had looked to be a star-crossed campaign. When the whistles blew to end both games, the math was unforgiving for the host nation: Switzerland and Norway were moving on, and New Zealand was out.

With that elimination, New Zealand became the first host ever eliminated in the group stage, a fate that Australia will try not to match in its own must-win game against Canada on Monday. Not even company will ease the sting for the Ferns, though.

Norway, on the other hand, will feel resurrected after a chilly night in Auckland. It had not particularly enjoyed the view from last place over the past week, not when it lost to New Zealand in its opener, not when its star Caroline Graham Hansen publicly challenged her coach to restore her to the lineup and then apologized for her outburst, not when the striker Ada Hegerberg sat out again with an injury.

Norway got on a roll.Credit…Abbie Parr/Associated Press

Faced with the humiliation of going out at the hands of the Philippines, though, something stirred in the Norwegians.

Forward Sophie Roman Haug scored on a one-time volley after only six minutes, then doubled her total with a header after only 17. Graham Hansen made it 3-0 before the half, then sent in the cross that was turned in for a Philippines own goal three minutes after halftime.

That silenced a profoundly pro-Philippines crowd of more than 34,000, and allowed Norway to set aside a week of grumbling and whispers of locker room discontent.

“We felt it was us against the world today and we performed from the very start, delivering when we really had to,” Norway Coach Hege Riise said. “This was the best response we could have given the Norwegian people and ourselves.”

Guro Reiten’s penalty made it five and then Roman Haug added her third, and Norway’s sixth, in injury time and that was that. But by then everyone knew it was over anyway, and the only outcome that mattered was the one in Dunedin, where New Zealand pressed and pressed for the goal that never came, the chance to change a scoreline the Ferns knew absolutely wouldn’t suffice.

When it didn’t arrive, when the whistle blew for full time, the players’ stunned faces told the story of a tournament that started brightly and, for them, is now over far too soon.