The Masters and US Open winner fell just one stroke short of claiming a place in a play-off after shooting a final-round 69 to finish 14 under at St Andrews.
The world number two could then only watch as Louis Oosthuizen, Marc Leishman and Zach Johnson battled it out over extra holes for the Claret Jug.
The 21-year-old told ESPN: “Right now it’s a tough feeling to be that close in a major. It does not matter about the historical element, to be that close on our biggest stage and come up short, how many chances do you get? It’s tough to swallow for a bit.
“My goal was four under for the round and we got there on 16. Ideally you can finish par, birdie and that would have got it done.
“It stings a little bit. We gave it a really good run but that was some phenomenal golf by those guys.”
Spieth would have become the youngest Open champion since 1893 but his bid for the title was undermined by a costly double bogey at the eighth, where he four-putted. He recovered to reach 15 under but was unable to save par on the notorious 17th and a wayward drive at the last cost him the chance of a closing birdie.
He said: “Today was a really tough day. I just made a mental mistake on number eight and it seemed to have cost me as well as on 18, just not giving myself a chance.
“Who would have thought a drive on 18 was going to be what really hurt me at the end there. It’s kind of hard to not hit a good one on that hole. I just wish I had given myself a little better opportunity.”
As for his troubles on the eighth hole, he said: “It was the hardest rain and the hardest wind at the same time of the day.
“When you look up from the ball and you’re getting pelted in the face it’s a hard shot, and I just tried to sling one in there and I left it 40 yards from the pin on the green there.
“On that hole I had left so many short throughout the week and I said, ‘I’m not leaving this one short’, I’m going to get this one up there, and instead hit it off the other side of the green where it was really dead. So that was a mental mistake on my part.”
Despite missing the chance to make history with regards the grand slam, and become the second youngest world number one ever, Spieth insisted he would soon get over his disappointment.
He will still have the chance to accomplish the rare feat – achieved only by Ben Hogan in 1953 and Tiger Woods in 2000 – of winning three majors in a year at the US PGA Championship next month.
Spieth said: “I don’t know how many guys have done three majors in a year. I’m sure there’s only been a few. So that would be the next goal as far as the history goes.
“I’ve got a couple of weeks off now and I’m going to go home and reflect on it. It won’t hurt too bad. It’s not like I really lost it on the last hole, and 17 was brutally challenging.
“I made a lot of the right decisions down the stretch and would certainly have closed plenty of tournaments out. This just wasn’t one of those.
“It’s hard to do that every single time and I won’t beat myself up too bad because I do understand that.”