Distraught New Zealand captain Sam Cane said he "would have to live forever" with the red card he received in the 12-11 defeat to South Africa in Saturday's Rugby World Cup final.

The 31-year-old sat pitchside looking astonished as referee Wayne Barnes waved a red card, upgrading the yellow he had initially been shown for a high tackle on Jesse Kriel.

Cane had hoped to make history by skippering the All Blacks to a record fourth title - instead he became the first player to be sent off in the sport's showpiece.

It was the Springbok captain Siya Kolisi, who had been yellow-carded himself early in the second half, who lifted the trophy.

For Kolisi it was a second time, for South Africa a record fourth.

"We have been at the tournament for two months and anything around the head has ramifications," Cane told reporters.

"I am not here to say whether it is right or wrong, it can't be changed.

"Unfortunately it is something I will have to live with forever."

Head coach Ian Foster was similarly downcast, though extremely proud of how his side had taken it to the wire despite playing one man down for around 50 minutes.

The 58-year-old was slightly bemused Cane had got red while Kolisi did not have his yellow card upgraded for a similar tackle.

"I don't want to be us talking about red cards," said Foster. "It is what it is.

"There will be a plenty of time to analyse that. The game has got a few issues it's got to sort out.

"That's not sour grapes. There were two similar incidents one was a red, one was a yellow (for Kolisi).

"That is the game."

Foster, though, was fulsome in his praise of the forlorn-looking Cane sitting beside him.

"I think we've all seen the way Sam has contributed to the game, our team behind the scenes, he's been fantastic, worthy of being captain of the All Blacks," said Foster.

"It is a fantastic honour and a privilege and I think he's carried that magnificently well and I am incredibly proud of him.

"It's a tough old day at the office when that happens and he'll be feeling a lot of emotion, I guess."

- 'Couldn't be more proud' -
Cane said he was still able to take in how well his teammates had stepped up after his dismissal.

"I'm feeling so much hurt, but I am so proud of the group the way they fought back and gave ourselves a shot of winning that game," he said.

"It speaks volumes for the group as a whole.

"It is a fantastic group of men who care so much for playing for the All Blacks and making New Zealand proud.

"So there is a lot of heartbreak in the sheds (dressing room) right now. It is hard."

The final was the third successive match the Springboks had won by just a point, having beaten hosts France 29-28 in the quarter-finals then England 16-15 in the semi-final.

Foster said it had been a "heck of a final" and praised the Springboks for their refusal to let go.

"They just know their game," he said.

"They are strong. Experienced. Clearly they have learned how to fight in a dark place.

"You can't argue with the three tight wins in this tournament."

Foster and Cane had a torrid time last year when the former's job was on the line until his captain and other players insisted he had to stay.

However, Foster is stepping down now as Scott Robertson has been named head coach -- Foster refused to re-apply for his job as he thought it was unnecessary to hold the process before the tournament.

He said he leaves with his head held high.

"I would say there were a lot more ups than downs," said Foster.

"I've been privileged to be with a special group of people.

"We lost but as a coach you want your team on the big stage and to put their best foot forward, which they did.

"I couldn't be more proud." (AFP)