Australia beat Indonesia 4-0 in their last-16 tie on Sunday while South Korea played 120 minutes against Saudi Arabia before prevailing on penalties late on Tuesday, giving Klinsmann's side only two days to recover before their quarter-final.
"Rest days are what it is, you accept it and move on. Now we are ready for this huge game and we're very hungry," Klinsmann told reporters.
"If you want to go through in a knockout phase of a big tournament, you have to be ready to suffer. You have to deal with pain because we got banged up in the last game and that's normal.
"It's normal and the players play this way in their club teams. Many of them play in Europe every three or four days, so no problem."
South Korea striker Cho Gue-sung said the lack of adequate rest could be a factor, but experience and mentality would be key.
"A lot of my teammates have plenty of experience... But I think at this moment in the tournament, it's more about mentality than physicality," said Cho, who scored a late equaliser to take the game against Saudi Arabia to penalties.
"The reality is I think mentality plays a bigger role now and we're just focused on achieving what we want to achieve.
"Australia is a very strong team, very solid in defence. They're very physical and they're big, but we have our strengths. There's no pressure on us, we have plenty of qualities, we have speed up front with very quick players."
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On the other hand, Australia coach Graham Arnold said the four-day rest period allowed him the luxury of giving his players some time off.
"I think one of the most important things in tournaments is downtime and making sure that the players keep their brain fresh and their mind clear," Arnold said.
"So we gave the boys a day off to recover after the Indonesia game and they are in real good spirits.
"Of course, I'll be ready for the battle. They've got depth in their squad, a lot of choices. But for us, the full focus is on ourselves."
Australia striker Mitchell Duke has great memories of playing in Al Janoub Stadium, where his header in a 1-0 win over Tunisia in November 2022 gave the side their first World Cup victory in 12 years.
"You look forward to the big games as a professional footballer," said Duke, who has fully recovered from a hamstring injury.
"That's where it comes down to big moments and big players can step up in those moments."
