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McIlroy began the day in a tie for the lead and was two shots ahead at the turn, but a closing bogey-free closing 70 proved insufficient to end his eight-year drought in the game’s biggest tournaments.
Smith fired eight birdies – including five in a row from the 10th – to card his second 64 of the week and finish 20 under par, beating the previous best of 19 under on the Old Course set by Tiger Woods in 2000.
“(I’m) disappointed obviously,” McIlroy said. “I felt like I didn’t do much wrong today, but I didn’t do much right either.
“It’s just one of those days where I played a really controlled round of golf. I did what I felt like I needed to just apart from (not) capitalising on the easier holes around the turn, nine, 12, 14.
“If I had made the birdies there from good positions, it probably would have been a different story.
“But, look, I got beaten by a better player this week; 20 under par for four rounds of golf around here is really, really impressive playing, especially to go out and shoot 64 today to get it done.
“I’ll rue a few missed putts that slid by, but it’s been a good week overall. I can’t be too despondent because of how this year’s going.
“I’m playing some of the best golf I’ve played in a long time. So it’s just a matter of keep knocking on the door, and eventually one will open.
“I’ll be okay. At the end of the day, it’s not life or death. I’ll have other chances to win the Open Championship and other chances to win majors. It’s one that I feel like I let slip away, but there will be other opportunities.
“I’ve just got to keep putting myself in position, keep putting myself in there. And whenever you put yourself in that shining light, you’re going to have to deal with setbacks and deal with failures.
“Today is one of those times. But I just have to dust myself off and come again and keep working hard and keep believing.”
McIlroy and his family were staying in a hotel overlooking the 18th hole of the Old Course and the 33-year-old admitted he kept imagining seeing his name on top of the leaderboard behind the green at the end of play on Sunday.
“I’m only human. I’m not a robot,” McIlroy said. “Of course you think about it, and you envision it, and you want to envision it.
“My hotel room is directly opposite the big yellow board on 18 there and every time I go out, I’m trying to envision McIlroy as the top name on that leaderboard and how did that feel?
“At the start of the day it was at the top, but at the start of tomorrow it won’t be. Of course you’ve got to let yourself dream.
“You’ve got to let yourself think about it and what it would be like, but once I was on the golf course, it was just the task at hand and trying to play the best golf I possibly could.”