Nick Kyrgios has been taught a lesson by the legendary Roger Federer in their third round showdown at the US Open.

Federer easily swept past Kyrgios 6-4 6-1 7-5 in their clash at New York's Arthur Ashe Stadium, a comprehensive victory which showed Kyrgios and the world why he is still considered one of the greatest in the game.

Kyrgios was gracious in defeat and seemed awed by his competitor's prowess, according to the Herald Sun.

“He was too good,” Kyrgios said.

“I think we're two very different characters,” said Kyrgios.

“But I think, you know, just the way he goes about things, I could take a leaf out of his book.

“The way he behaves on court, his demeanour. He's the ultimate role model to anyone who wants to play.”

Federer was less complimentary of his younger, notoriously tumultuous opponent, criticising Kyrgios for attempting a fanciful drop shot at a crucial moment within the third set.

“He should have hit a normal forehand in the open court and he chooses to go for sort of the drop shot, which at the end cost him the match,” Federer said after the match.

“So clearly when you play that way and you lose, it's always, like, you feel like he's so much to blame, but that's just how he plays.

“But today I think he didn't come up with the goods when he really had to, and I was good, I think, by making him hit that extra shot.”

Kyrgios returns home unsatisfied with his performance, and hopeful that his career will take a turn for the better. He is yet to improve on his quarter final run at Wimbledon in 2014, which proved the 23-year-old could compete with the best.

“In my career, I have been around for about four years now. I have barely done anything. I think I can do a lot more.”

While Kyrgios is facing a long trip home, John Millman's dream US Open run has continued.

The relatively unknown Aussie has advanced into the fourth round of the Open, and is set to face down Federer on Tuesday at the Arthur Ashe Stadium.

Millman has never before advanced past the first week of a Grand Slam and his success in New York is the deserved result of years of hard work.

Millman is the sole Australian singles competitor remaining in the Open, with Ashleigh Barty and Alex de Minaur shot down in the fourth and third rounds respectively.