The rematch will take place on December 21 in Riyadh, Saudi Arabia, with the WBC, WBO and WBA titles on the line
The treble-chasing All Blacks suffered only their second defeat in 17 matches against England as their astonishing 18-match unbeaten run at the World Cup came to a shuddering halt in Yokohama on Saturday.
"Nothing will alleviate the pain," said Hansen, whose seven-year reign as coach ends after next week's third-place playoff.
"You've got to bank that. We're still hurting as you'd expect, I'm sure the whole country's hurting. It's gut-wrenching, but when you lose you need to show humility - bite down on your gum shield and suck it up," he added.
"You measure your character on how you deal with adversity."
Hansen, who has been linked with the director of rugby role at Japanese club Toyota Verblitz, paid tribute to England after they beat the All Blacks for the first time in four attempts at the World Cup, revealing he had shared a beer with his old rival Eddie Jones after the game.
"England didn't sneak up and hit us in the face," he said, noting how desperate England have been to exorcise the demons of their 2015 flop when they became the first host side to crash out in the pool stage.
"They were a team coming into this tournament with a massive amount of pain themselves - not making the playoffs in their home tournament hurt them.
"They worked their butts off. They don't play a sophisticated game: win the ball, give it to a big bloke and run hard. It's simplistic but it's beautiful," added Hansen.
"We were beaten by a better team."
Kieran Read still appeared shaken after failing to lead the All Blacks to a third successive title in his sign-off as captain.
"It's a bitter pill to swallow," said the Toyota-bound number eight, whose 34th birthday had been ruined by a rampaging England side.
"Your family, the ones closest to you go through that too," added Read after his 126th Test ended in a first World Cup defeat.
"It was my birthday yesterday and I get back to the hotel and there's messages from my kids - it puts things in perspective. My kids aren't going to love me any less."
After failing to emulate predecessor Richie McCaw, who lifted two World Cups with New Zealand, Read tipped the All Blacks to come back stronger.
"It's pretty empty, we're gutted," he said of his emotions the morning after.
"But it's not going to define us as a group. The younger guys have an opportunity to come back in four years. They'll hold on to this feeling and come back."
Hansen backed the All Blacks to "get back on the horse" quickly after their stunning exit.
"It's massively important," he said. "There hasn't been a lot of adversity. For 12 years we've been successful - we've maybe dropped 10 games now out of 104 or 105 games.
"When you lose you find the inconvenient facts, that maybe you've been sandpapering over some things. There will be a lot of lessons to learn."
The rematch will take place on December 21 in Riyadh, Saudi Arabia, with the WBC, WBO and WBA titles on the line
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