With spectators chanting his name, Woods made a spirited run at a 15th major championship but couldn't make up a 4-stroke deficit on Brooks Koepka, who shot a 4-under 66 to win the PGA Championship for his second major this year and third overall.
"Crowds are incredible", said Italian golfer Francesco Molinari.
"That being said, (Bellerive) isn't the same as Le Golf National". "It was the first time Tiger has been in contention and I've been in contention at the same time, so the fans definitely let you know what he was doing".
Over an ear-splitting afternoon in which most of the cheers weren't for him, Brooks Koepka got a taste of what golf feels like when Tiger Woods is in the hunt.
On the European side, qualifying runs for another three weeks before captain Thomas Bjorn makes his four picks in September.
The eighth and final automatic qualifying spot was still in limbo going into the PGA Championship, and Webb Simpson held on to secure his trip to Paris. Despite the hole playing under 300 yards, Woods made a decision to lay up and not risk hitting into the water to the right of the green.
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Not only did Tiger finish second at the PGA Championship, but he was also tied for sixth at The Open Championship.
"These fans were so positive all week".
And yet Thomas and the rest of his Tour colleagues are very aware of just how special Koepka is, and how insane it is that someone with four PGA Tour wins has claimed three of the last six major titles.
His 2018 campaign has taken everyone by surprise and came close to winning his first PGA Tour event in five years at the Valspar Championship, finishing one-shot back.
The last one was a laser of a 4-iron from 248 yards that settled 6 feet away, sending him to a dream finish of a year that began with the 28-year-old Floridian wondering if a wrist injury that kept him out four months would ever allow him to compete again.
That par was the most disappointing of the 10 straight Woods made to finish his third round Saturday at the PGA Championship.
"I played 29 holes, I think I dropped three shots today and two of those were three-putts". "Bit of a struggle with my game".
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The World Cup victor took straight to Twitter when the club's official account reported the comments replying, "Oops". "But I am happy with the players because they run and they fight, and also we need (to) continue working tactically".
"Making that putt at least gave me a chance", Woods said.
Crowds cheered the veteran through a thrilling round that saw him miss every front-nine fairway but take only 10 putts, scrambling from dirt, trees and bunkers to stay in the hunt.
British Open champion Francesco Molinari is in a three-strong group on seven-under, the Italian continuing the fine form he showed at Carnoustie last month.
"Oh, God: I didn't know if I was going to play golf again, so, yeah", he said, later adding, "I hadn't played in two years (before this year)".
The impact was dramatic for rivals as well.
British Open victor Francesco Molinari of Italy and England's Justin Rose, Tyrrell Hatton and Tommy Fleetwood helped secure their lead in the European points spots with solid showings at the PGA, Molinari sharing sixth and Hatton sharing 10th.
"So I had to kind of figure this out on my own, and it's been really hard, it's a lot harder than people think".
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Another to disappoint was Northern Ireland's Rory McIlroy, who finished back on two under, stretching his drought in the majors to four years.
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