Britain's Dan Evans says he "got a good, healthy lesson" after being outclassed by second seed Daniil Medvedev in the US Open last 16.

Medvedev, 25, has not dropped a set at this tournament and the British number one never got close to changing that under the roof on Arthur Ashe Stadium.

"He was a different level to me today," Evans, 31, said.

Asked what he had learned from the encounter, the Briton replied with a smile: "You're looking at the draw hoping he's nowhere near me for the rest of my days."

World number two Medvedev will play qualifier Botic van de Zandschulp for a place in the semi-finals after the Dutchman stunned 11th seed Diego Schwartzman.

Evans beaten but takes home positives

By reaching the fourth round in New York, 31-year-old Evans had matched his previous best Grand Slam performance and is set to reach a career-high ranking inside the world's top 25 when the list is next published after the US Open.

After some disappointing results at the other three Grand Slams of the year, losing in the first round at the Australian and French Opens and the third round at Wimbledon, and having missed the Tokyo Olympics because he contracted Covid-19, this tournament has been uplifting for both him and British tennis fans.

"It's a good week. It was difficult - some difficult matches," he said. "But it was a solid, solid week. [I am] happy with how I dealt with the conditions. The whole trip in itself was difficult. I played my best tennis this week, which is pleasing."

In the previous round he had to fight back from two sets down to beat Alexei Popyrin and against Medvedev he once again showed glimpses of his grit.

Facing set point on his serve at 5-2 in the opener, Evans saved it with a wonderful point where he hit an angled volley at the net before rushing back to successfully unleash a smash that meant he forced Medvedev to serve out the set.

But the Briton was then broken to love in the first game of the second to give the Russian an early advantage that he never looked like relinquishing.

Evans was in danger of letting the Russian go a double break up for 3-0 but fought back from 15-40 down to stay in touch and then got a break back for 3-3.

But he immediately found himself behind again after two double faults contributed to a soft break of his serve. Medvedev wasted no time in making the break count as he eventually went on to serve out the set with a rapid game that included two aces and one unreturnable second serve.

Evans put up little resistance in the third as Medvedev broke early and then again to love to wrap up a clinical victory in a swift one hour and 45 minutes.

Evans will now head to tournaments in San Diego and Indian Wells and although he said he was not focused on rankings, he admitted he would "love to be in that bracket" of the world's top 20 by the end of the season.

"For sure I need some rest," he said. "To move in the direction I want to be moving, there's some more hard work left this year.

"I'll see how the next few days look. [I'm] nursing a bit of soreness," added Evans, who retired from the doubles as a precaution before his third-round singles match. "See how long that takes, then move on from there."

Medvedev marches on

The early exits of leading players including third seed Stefanos Tsitsipas, fifth seed Andrey Rublev and eighth seed Casper Ruud has opened up this half of the draw for Medvedev, who is seeking a maiden Grand Slam title.

Having not lost more than four games in a set at the tournament, he is displaying why he has been hotly tipped to be the man who could derail Novak Djokovic's bid for a calendar Grand Slam.

Medvedev was imperious on serve, hammering down 13 aces and winning 84% of first-serve points, but it was one of his service returns that he dubbed "the best shot of the match".

He was in fact so impressed with the shot - a stunning round-the-net forehand return that kissed the line - that he gestured for the crowd to make more noise in appreciation for it at the time.

There were plenty of other instances when there was no need to ask for admiration as the Russian unleashed 43 winners in a devastating performance.

Medvedev is clear with his aims in New York, where he is seeking to shake off the disappointment of a quarter-final defeat at the Olympics last month by improving on being runner-up to Rafael Nadal here two years ago.

"I just want to make it to the final again to make some more memories - and hopefully a better one [this time]," said Medvedev, who lost in five sets to the Spanish 20-time Grand Slam champion in that final.