Hideki Matsuyama believes he is edging closer to his dream of winning a first major after a sparkling final round left him just short at the US Open on Sunday.

Matsuyama fired the lowest final round of the day, a six-under-par 66 to finish four shots adrift of winner Brooks Koepka at Erin Hills.

The world No 4's round contained eight birdies and two bogeys but ultimately it was not enough to reel in the leaders.

Matsuyama, who also shot a second round 65, ultimately paid the price for a wayward opening 74 on Thursday and a faltering second round 71.

"If I learned anything, you've got to put four good rounds together," Matsuyama said afterwards.

"I played two good rounds, but it wasn't enough."

"No regrets, I did play well. Just came up a little short."

Matsuyama earlier produced some inspired golf to raise hopes of an improbable victory after he had begun the day six off the pace.

The Japanese world No 4 rattled off three quick birdies in his opening five holes, which included an incredible 41ft putt on the second to launch his charge.

But even though he rattled in five birdies on the back nine, Koepka was always able to keep the Japanese at arm's length as he waited in the clubhouse.

Matsuyama has now posted top 10 finishes in each of the four majors and says this week's experience will help as he prepares to take a crack at the Open Championship next month and the PGA Championship in August.

"I learned a lot this week," he said. "Hopefully, though, in the future, in majors, I can play in the either last or next to last group to give myself a better chance.

"But I'm happy with the way I played, and it gives me confidence going forward."