The Red Roses had three years of complete dominance and a 30-match winning streak snapped by a 34-31 loss to the Black Ferns after playing for 62 minutes with 14 women at Eden Park.
"I thought the girls left everything out there. Sixty minutes with our backs to the wall, to keep fighting and to be in with a shot to win it right at the end," said Hunter, who was playing a record-extending 140th test.
"You could not have asked for more from the girls, it's a very special group and we can be immensely proud of what we've done for the women's game.
"It will hurt, we don't want to be losing World Cup finals, especially in the manner that we've done, but I'm so, so proud of what we've done."
The loose forward said "when the dust settled", she would be proud to have been part of such a magnificent exhibition for women's rugby.
"You can't expect nations not to invest in their teams after you've put on a showcase in a final in front of 40-odd thousand people," Hunter added.
"It's come to the party, isn't it? People have finally woken up to what women's rugby is all about. Hopefully, that will ignite other nations to go 'we need to invest in our women's game and make it a level playing field'."
Like Hunter, coach Simon Middleton paid tribute to New Zealand for their sixth World Cup triumph and said there would be no recriminations for winger Lydia Thompson for being sent off for a reckless challenge on Portia Woodman.
"She's pretty upset as you might imagine, but she is one of the best pros and nicest people you are ever likely to meet," he said with Hunter nodding along.
England women have inspired the nation, says Jones
The Red Roses should be proud of what they have achieved on and off the pitch, England men's coach Eddie Jones said.
The loss marks the second upset in major finals for England after their defeat by South Africa in the 2019 men's World Cup but Jones said the Red Roses are "excellent ambassadors" who will inspire more youngsters to take up the sport.
"We know how tough this moment is and it will be hard to feel the positives in the immediacy but they should be very proud of what they've achieved on the pitch and off it," Jones said in a statement.
"They've played excellent rugby, had an unbelievable unbeaten run and are a really tight group," Australian Jones added.
"Back here in England we can feel the impact that they have made across the game; how many people are talking about them and enjoying watching them and they will inspire even more girls and boys to play rugby."
England host the next women's World Cup in 2025.
