The Springboks held out to claim a record fourth World Cup crown, with Siya Kolisi the second man to lift the Webb Ellis Cup twice.
All Blacks captain Cane was sent off for a head-high shot on Springboks centre Jesse Kriel.
Cane himself though simply conceded that he will never be able to rid himself of the shadow of the dismissal.
“There’s just so much hurt right now, it’s actually hard to find the words to explain it,” said Cane.
“But it’s so, so hard because you’re feeling so much hurt but you’re also so proud.
“It’s something unfortunately I’m going to have to live with forever.
“At the time I wasn’t even aware, it caught me off guard the fact he’s stepped back.
“Anything around the head has ramifications and I’m not here to discuss whether it was right or wrong, it can’t be changed.
“We still gave ourselves a good shot of winning that game. It speaks volumes of the group as a whole, the group of men who care so much about playing for the All Blacks and making New Zealand proud.
“There’s a lot of heartbreak in the sheds right now, and it’s hard.”
All Blacks boss Foster insisted he was not talking through the bitterness of defeat, but he suggested the officials did not judge two opposition situations the same way.
Cane was sent off for his head-high shot, while Kolisi was sin-binned for a head-to-head collision with Ardie Savea.
The officials appeared to deliver the right calls on those two issues, but Foster was left unhappy.
The All Blacks boss also hinted at general unhappiness with Television Match Official (TMO) Tom Foley.
“I really don’t want the game to be us talking about red cards. It is what it is,” said Foster.
“There was an attempt to wrap [from Cane], there didn’t seem to be much force in the contact.
“The other card, there was a lot of force in the contact. The game’s got a few issues it’s got to sort out.
“It’s not sour grapes, but there are two situations with different variables, one’s a red card, one’s a yellow card – and that’s the game.
“We got the same behaviour from that TMO in the Irish series last year. So we expected what we got.”
Foster hailed Cane for his leadership of the All Blacks, in spite of the red card.
“I think we’ve all seen the way Sam’s contributed to the game and our team behind the scenes and it’s been fantastic,” said Foster.
“He's fully worthy of being captain of the All Blacks which is a fantastic honour and privilege.
“I’m incredibly proud of him and proud to coach him. It’s a tough old day at the office when that happens. And we’ll be feeling a lot of emotion I guess.
“The heart and soul the team showed afterwards, that’s largely due to the spirit of the group, even though Sam wasn’t on he was still a big part of that.”