Rory McIlroy just missed out on a medal after a play-off while Shane Lowry said he was "very disappointed" with his final day of play at the Olympic Games.
The USA's Xander Schauffele won gold and Rory Sabbatini claimed silver for Slovakia.
McIlroy had a chance on 18 to move to 16-under, but his putt slipped centimetres by the hole and it meant he was into a seven-person play-off.
The County Down man made it as far as the third extra hole, and had the best tee shot of the remaining four players at that stage. His approach left him a putt of seven foot, but he couldn't make it as Collin Morikawa and CT Pan remained in the play-off, with Chinese Taipei player Pan eventually taking the medal.
"I never tried so hard in my life to finish third - I gave it my all out there today," McIlroy told RTÉ Sport afterwards.
"I played the last two holes in regulation really well. I thought I played well in the play-off. A good par on 18 (the first play-off hole) to keep it going.
"I had a good chance there on the third play-off hole and it just slipped by on the right.
"I'm proud of how I played this week and how I competed. I'll look back at this week with great memories. It's been brilliant.
"Everything about it - it's not just another golf tournament. You're a part of something much bigger and I'm really looking forward to Paris in three years' time.
"Hopefully Shane and I make the team again because I've really enjoyed his company this week - a throwback to our amateur days."
Lowry started the day on 10-under par but a 71 meant he also finished the day there - only good enough for a tie for 22nd place.
It took him 39 to get to the turn, as he double bogeyed the par-four ninth. Although he managed three birdies in his last five holes it wasn't enough to get into contention for a medal.
"I'm very disappointed, to be honest," he told RTÉ Sport afterwards.
"I went out there to do a job today and I didn't do it. It's so disappointing. I feel like I was playing the golf to do it. I played good enough all week and then today on the front nine I just didn't have it - I played lovely on the back nine.
"It's tough to take - it is - because I went out there and I really wanted to win a medal for everyone back home. It was more for everyone back home than it was for me. I had visions of bringing it home and seeing everyone back home."
Reflecting on his first experience of an Olympic Games, Lowry acknowledged that it felt different from other tournaments.
"I was anxious going out there today - I felt it. I knew how much it meant. I'd never been to the Olympics and you don't know what to expect. You know it's going to be different to every other event but when I got here it felt like a big deal.
"I wanted all week to put one of those medals around my neck this afternoon but I didn't do it.
"My year has been going and I feel like I've been playing well. But I haven't been putting four good scores together and that's why I haven't won a tournament."
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For many competing in the Olympics is the highlight of their sporting career but Lowry has some big events to look forward to this year, including a potential debut at the Ryder Cup next month at Whistling Straights.
"I'm lucky with my sport that I've got a lot of big weeks ahead of me coming up. I've a couple of days to relax and reset and then move onto the next tournament."
McIlroy is preparing for his sixth Ryder Cup and he says he'd like to partner up with Lowry again in the battle between Europe and the USA.
The former world number one joked, "If Padraig is looking for someone to take a rookie around I wouldn't mind pairing up with Shane!"
'I never tried so hard in my life to finish third' - @McIlroyRory on his 'brilliant' Olympic experience, which just came up short of a medal.#tokyo2020 #RTESport #golf #olympics— RTÉ Sport (@RTEsport) August 1, 2021
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