Cane made history during the 12-11 defeat to South Africa in Paris on Saturday by becoming the first player to receive a red card in a Rugby World Cup final.
The All Blacks were greeted by a small crowd at Auckland Airport when they arrived home in New Zealand.
Cane said the level of good wishes from their fans during the tournament in France had been overwhelming.
"The support is something I haven't experienced as an All Black," Cane told reporters.
"It's the best I've found and that's from halfway around the world.
"I said before the final it's been overwhelming. And put it this way, I've been pleasantly surprised with the support post the final, too.
"I felt like I let a lot of people down and feeling that support has certainly helped. On a personal level, I appreciate all the kind words. It means a heck of a lot."
Cane looked shell-shocked during the final when the yellow card he initially received for a high tackle on Jesse Kriel was upgraded to a red.
The New Zealand skipper said some motherly advice has since helped him come to terms with the dismissal.
"My mum actually said to me if it was my boy (son) who'd been in this situation, 'how would you want him to feel and you wouldn’t want him to beat himself up', so (I'm) trying not to be too hard on myself," he added.
All Blacks number eight Ardie Savea, named World Rugby Player of the Year on Sunday, said it was a "bittersweet" moment to be greeted by crowds of fans without the World Cup trophy.
Savea relived the final during the flight home. "Playing the game over in your head, which is normal after losing a really big one," he said. "It will hurt for a little bit."
Ian Foster, who has bowed out after four years as All Blacks head coach, said he was "immensely proud" of their run to the final.
The 58-year-old declined to comment on whether he was interested in the Australia head coach position, vacant since the resignation of Eddie Jones earlier this week.
