Tiger Woods finishes in the top 10 at The Open

Tiger on Open loss: 'Ticked off at myself' (1:30)

Tiger Woods reviews his missteps at the 11th and 12th holes that caused him to fall short of capturing his 15th major championship. (1:30)

CARNOUSTIE, Scotland -- His name atop the leaderboard, Tiger Woods reached into the past for the magic that had been missing for so long, a push to a major title that even he at times wondered if ever were possible.

Woods led The Open at Carnoustie on Sunday, carnage occurring all around him, his two early birdies and some deft par saves putting him in position for a 15th major championship.

But the golf gods did not comply, and Woods was unable to sustain what would have been one of golf's all-time tales, his major hopes derailed by the long fescue rough on one of the hardest links in the world.

Woods, 42, settled for a final-round 71 and finished three strokes behind Italy's Francesco Molinari -- with whom he played the final round -- ending up in a tie for sixth.

A consolation is moving to 50th in the world for the first time since January of 2015 and qualifying for the WGC-Bridgestone Invitational in two weeks.

"A little ticked off at myself for sure,'' said Woods, who held the lead alone when he stood on the 11th tee. "I had a chance starting the back nine to do something, and I didn't do it. I thought 9 [under] would be the number.

"Next thing, lo and behold, I'm tied for the lead, and then I'm leading it.''

But Woods, who led the field in driving accuracy through three rounds, misfired with a 3-iron off the tee at the par-4 11th.

Playing from tall, wispy rough, he experienced what many do when finding that type of grass on a links: it grabbed the shaft, his clubface closed, and his approach sailed well left of the green.

The ball bounded into spectators and actually caromed back toward the green. But Woods was behind a bunker, tried to cut it too close with a flop shot and missed the green. He ended up with a deflating double-bogey that knocked him out of the lead. And then he followed it with another missed fairway with an iron at the 12th, leading to a crushing bogey.

There is plenty of room to debate his strategy. Another club off the tee? Pitching back to the fairway instead of going for the green? Playing a safe shot from behind the 11th green?

But Woods would not go there, saying, "I did everything the way I thought I needed to do it to win the championship. There were a bunch of guys with a chance to win, and I was one of them.''

Woods began the final round 3 strokes behind Jordan Spieth, Xander Schauffele and Kevin Kisner. Amazingly, all three of those players made double-bogeys over the first seven holes; Spieth, the defending champion, shot 76 to drop to a tie for ninth. Schauffele ended up in a tie for second, two shots back of Molinari, as did Kisner.

It was Molinari who didn't make a mistake, shooting a final-round 69 and playing the final 37 holes of the tournament without a bogey.

Woods was there for all of it, and it's a tribute to Molinari that he did not flinch in the presence of one of the game's most popular -- and followed -- players.

"It was a blast,'' Woods said. "I was saying earlier that I need to try and keep it in perspective because the beginning of the year, if they'd have said you're playing The Open Championship, I would have said I'd be very lucky to do that.

"I talked to Serena [Williams, last week at Wimbledon]. I'm sure she'll probably call me and talk to me about it, because you've got to put things in perspective. She just had a baby and lost the Wimbledon finals. Just keep it in perspective, and the same thing with me.

"I know it's going to sting for a little bit here, but given where I was to where I'm at now ... blessed.''

Woods had not played The Open since missing the cut at St. Andrews in 2015. This was just his ninth major championship in the past four years. He tied for 32nd at the Masters and missed the cut at the U.S. Open but now has six top-12 finishes in 12 events.

When he birdied the 14th hole Sunday, that gave him an outside chance at getting back into the tournament, as he trailed by just 2 strokes. But the closing holes are treacherous, and despite flinching on a tee shot at the 18th because of a spectator bellowing during his backswing, he managed to give himself a 5-footer for birdie that he missed.

As it turned out, that birdie would have just briefly brought him to within 1 stroke -- as Molinari made his putt for birdie to seal the tournament.

"It didn't feel any different,'' Woods said. "It didn't feel any different to be next to the lead and knowing what I needed to do. I've done it so many different ways. It felt great to be part of the mix and build my way into the championship. Today was a day I had a great opportunity.''

Bidding to win his 15th major 40 years removed from Jack Nicklaus doing the same thing in 1978 at St. Andrews, Woods had not been in this position in years. The 4-shot final-round deficit was his closest to the lead in a major since the 2013 Open at Muirfield, where he was 2 back but tied for sixth. Also that year he tied for fourth at the Masters.

When Woods finished, he thought he had blown his opportunity to get to the World Golf Championship event in two weeks at Firestone, where he has won eight times. This is the last year the event will be played there, and Woods made it a goal to return.

To do so, he needed to be among the top 50 by Sunday, one of the qualifying cutoffs for the event.

He made it by .0122 ranking points, and he now sets up for a busy time with the WGC followed by the PGA Championship at Bellerive. Then two weeks after that, it is the FedEx Cup playoffs.