Erin, United States (AFP) - 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.

He 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 Japanese 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 an impressive second round (65), ultimately paid the price for a wayward opening round (74) on Thursday and a faltering third round ( 71).

"If I learnt anything, you've got to put four good rounds together," he 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 rattled off three quick birdies in his opening five holes, which included an incredible 41-foot 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 him at arms 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 in July and the PGA Championship in August.

"I learnt 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."