Kapur, who plies his trade on the Asian Tour, birdied six of his first seven holes on Thursday but couldn't keep up the momentum in the second and third rounds.
Indian golfer Shiv Kapur lives brief leaderboard dream at British Open
It was only for a fleeting period, but seeing his name at the top of the leaderboard at the British Open was a magical moment for Indian golfer Shiv Kapur.
A strong start to his opening round of Thursday saw him birdie six of the first seven holes before he eventually finished with a 3-under 68.
That was as good as it got for Kapur, after shooting 77 in the second round and 83 on Saturday.
Playing in the tournament for the second time since 2006, Kapur restored some pride when he made a 15-foot birdie putt on the last to end his week at Muirfield with a 71 and a total of 15-over par.
"It is easy to pick out the best moment," he said. "It had to be when I saw Kapur leading in the best tournament in the world.
"For years and years, I've watched the Open and I thought it would be nice to have my name on that yellow leaderboard. That dream came true, though momentarily.
"I learnt a lot, it has been a great experience and I won't trade it with anything. It was great to be on top the leaderboard and great to learn from yesterday."
Kapur, who plies his trade on the Asian Tour and is 14th in this year's Order of Merit, said he wanted to build on his experiences at Muirfield.
"It gave me a lot of confidence knowing that I can be up there on the leaderboard, because it shows that I can compete with the best players," he said.
"I just need to be more consistent and sharpen each area of my game a little bit so that I can be right there in the mix.
"I started on such a high with the adrenalin rush. Yesterday was a bit of a disappointment when I got off to a rough start, but I finished with a little bit of pride.
"You don't want to walk off the 18 green with drooping shoulders and not being happy with what you've done.
"I'm glad the bad round was yesterday and not today so I can walk away with a smile."
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