The Australian went toe-to-toe with Khachanov but did not do enough to counter the Russian's punishing serve as he fell 7-5 4-6 7-5 6-7(3) 6-4 to end his bid for a maiden Grand Slam title.
"I'm just devastated obviously," Kyrgios told reporters
"Just feel like it was either winning it all or nothing at all, to be honest. I feel like I've just failed at this event right now."
Kyrgios said Khachanov, who saved seven of the nine break points he faced, was the better player in the biggest moments as the 27th seed punched his ticket to a Grand Slam semi-final for the first time.
Wimbledon finalist Kyrgios had knocked out world number one Daniil Medvedev in the previous round but said lifting the trophy was all that mattered.
"All people remember at a Grand Slam, whether you win or you lose," he said.
"I think pretty much every other tournament during the year is a waste of time really. You should just run up and show up at a Grand Slam. That's what you're remembered by."
Sent packing at the final major of the year, Kyrgios said it will be an agonizing wait until the Australian Open kicks off the Grand Slam season next year.
"It's just like you got to start it all again ... It's just devastating," he said.
"It's heartbreaking. Not just for me, but for everyone that I know that wants me to win."
