The back-to-back champion finished the day on nine over par overall following his 76.
That left him 13 shots behind leader Tom Watson and ended the Irishman's hopes of a record-equalling third straight title.
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Harrington said: "I knew it was going to happen someday but it still hurts. I played poorly and just didn't feel I was on top of the golf course at all.
"It wasn't my day. I needed things to go my way if I was to challenge and they didn't. As soon as I bogeyed seven I knew The Open was lost."
Harrington, winner at Carnoustie and Birkdale in the past two years, admitted his well-documented swing struggles going into The Open left him short of confidence.
He admitted: "I wasn't surprised I wasn't better mentally. I made wrong decisions and in wind like this and on a course like this, you need to have things going for you.
"But I made too many mistakes, mentally, and made errors. I was worried about going for shots.
"I didn't think being eight shots behind was insurmountable on this links course - but after that I've got no chance.
"It will feel strange waking up tomorrow knowing I'm not in with a chance of winning. Then again, I play 30 events a year, and for 26 of them, I wake up on a Sunday morning thinking that!
"But this is The Open and it's a very big deal. So of course it hurts. But I'll get over it."
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