The Englishman began the day six shots behind eventual winner Shane Lowry and was not able to close the gap in difficult conditions at Royal Portrush.
Lowry, who won the 2009 Irish Open as an amateur in similarly poor weather, looked in total control before a combination of three bogeys and Fleetwood's birdie on the 12th cut the gap to four.
However, Fleetwood could not turn the screw and double bogeyed the 14th after finding sand off the tee, meaning Lowry increased his lead to five despite failing to save par from over the green.
Fleetwood was not only bidding to win his first major, but there he was also hoping to become the first English winner of The Open since Nick Faldo in 1992.
"That's the consolation, how well Shane did and how well he played," he told Sky Sports as he battled to hold back his emotions.
"It hurts," he added. "It's sore at the moment, but it's six shots back, it feels closer than that.
"It was Shane's time and Shane's week, so fair play," he added.
"I played well early on, the margins, putts on one, two and three, I hit a great shot at four and five. I was still in the game at 14.
"If Shane had made bogey. It's nice to still be in the Open with six or seven holes to go. It's difficult to stay in it.
"The mountain was a bit too high to climb. I hope so, the last three days, there was something about this week I felt like I had a chance. There was something about it.
"You get a sense maybe. I hope it's a matter of time, you never know what this game will give you. I'll look back at this and take the positives."
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