SOUTHAMPTON, N.Y. – In the end, Tommy Fleetwood needed a 62.

Fleetwood, the European PGA Tour star seeking the same kind of success in the United States, became the sixth player in U.S. Open history to shoot a 63, doing it Sunday at Shinnecock Hills Golf Club. But he left the course lamenting an eight-foot birdie putt he missed at the 18th for a record 62.

However, about 2 ½ hours after he finished, after Brooks Koepka holed his final putt for a 1-stroke victory, Fleetwood  didn't feel too badly.

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"The putt on 18, I actually wanted it more for the 62 at the time, and then it became a thing in the tournament," the 27-year-old Englishman said. "Obviously that's the putt that will play on your mind because that was the last shot you hit and that was your chance.

"I'm not going to dwell too much on it. It is what it is, but again I got very close to winning a major."

Fleetwood, who finished fourth in the Open last year at Erin Hills, looked to have shot himself out of the championship on Saturday when he came in with a 78 in the windy conditions. But he shot 3 under on the front, then ran off four straight birdies from holes 12 through 15 to get to 7 under for his round.

He had looks at birdie on his last three holes but couldn't get a putt to fall.

"If the conditions were a bit more like yesterday I'd have felt a little more comfy in the clubhouse," he said. "I'd have felt like I had a bit more of a chance. But the best players in the world are trying to win a U.S. Open, and you've got nothing but respect for how well Brooks did just to hole the putts at the right time."

Reed’s run

Patrick Reed looked to make a little history of his own Sunday.

The 2018 Masters champion birdied five of his seven holes and held a lead at one point early in the final round. But he fell short of picking up his second major of the year, shooting 3 over the rest of the way with one birdie and finishing fourth at 284.

"Of course it's disappointing," he said after his 68, "but at the same time, I tied for second at the PGA last year, won Augusta, then a top five here. My last three majors, to have a chance to really win all three of them and close one off, it means a lot.

"Of course, Grand Slam would have been nice. But honestly, to me, that was really the last thing on my mind. It was go out, played some solid golf, try to post a number and see if you can get the job done."

Co-low amateurs

Matt Parziale, the golfing firefighter from Brockton, Mass., and LSU star Luis Gagne tied for low amateur honors at 16-over-par 296.

Parziale, who was a professional golfer for three years before filing for amateur reinstatement and joining the Brockton Fire Department, shot a 75 and Gagne had a 74.

"I was happy to play well all four days," Parziale said. "I wouldn't say I played great. I played pretty steady for four days. Rounds can obviously always be better at all times, but I'm happy with the way I stayed in it."

Gagne, entering his senior year at LSU, had an interesting road to the Open. Both he and Cristian DiMarco left a local qualifier in Orlando before it ended and it turned out that they needed to play off for the final available spot. Gagne won the berth on a coin flip, then advanced through sectional qualifying to the Open.

"I learned a lot," he said of his week. "One thing is knowing that I can play with these guys. I still have a lot of work to do to be able to be out here. Knowing that I'm working on the right things and my skill level's right with these guys, it gives me a lot of confidence."