Kapur's final round 71, following up on 68, 77 and 83 on the first three days gave him a total of 15-over 299.
"I started Thursday on such a high with the adrenaline 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 and my head held high today," said Kapur about the week.
Kapur started out in first group with former Open champion, Sandy Lyle. He had finished by the time the leaders had teed off.
"The birdie on the 18th today felt good," said Kapur.
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After having no birdies on third day, he had four on the final day and it included a 15-footer on the last. His other three birdies were on third, fifth and ninth.
"There is a lot of positives I will take from this event. The front nine on first day showed me that I could play a higher level, but Saturday also showed me that I have lots to learn, especially about Links golf. And today was a matter of restoring pride," added Kapur.
Of his experience at the event, Kapur said, "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.
"It is easy to pick out the best moment. 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."