Cane's yellow card for a dangerous tackle on Jesse Kriel in the 28th minute of Saturday's dramatic clash at the Stade de France was upgraded to red by the bunker review system.
It was the first time a player had been dismissed in a men's World Cup final and although the All Blacks showed heart to overcome the setback and score through Beauden Barrett, they could not pierce South Africa's defence again.
Referee Wayne Barnes shows the red card to All Blacks captain Sam Cane in the Rugby World Cup final.
"It's hard because you are feeling so much hurt, but at the same time you are so proud of the group in how they fought back," Cane said.
"We really gave ourselves a good shot of winning that game; it speaks volumes of the group as a whole."
A despondent Cane refused to blame the officials, led by referee Wayne Barnes, or the bunker review system for a decision that left New Zealand swimming against the tide as the Springboks clinched a fourth World Cup title.
"At the time, I wasn't even aware (of the head contact). It sort of caught me off guard because of the fact he stepped back," Cane said.
"But we've been at this tournament for two months now and anything around the head has ramifications.
"I'm not here to discuss whether it was right or wrong. It can't be changed.
"It's something unfortunately I am going to have to live with forever."
Head coach Ian Foster (l) defended All Blacks captain Sam Cane after his World Cup final red card.
New Zealand head coach Ian Foster stood by his skipper and insisted the high tackle was not a red card offence, adding Siya Kolisi's challenge on Ardie Savea in the second half - for which South Africa's captain received a yellow - was equally severe.
"We've all seen the way Sam has contributed to the game, to our team behind the scenes, and it's fantastic," Foster said.
"He's worthy of being captain of the All Blacks, which is an honour and a privilege, and he has carried that magnificently.
"I'm incredibly proud of him and proud to coach him.
"There was an intent to wrap and there didn't seem to be a whole lot of force in the contact. The hit on Ardie had a lot of force ... and had a direct contact on the head.
"The game has a few issues it has got to sort out. That's not sour grapes."
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