Henrik Stenson closed with a 63 to win by three shots.
No losers here, but only one victor.
The American left-hander shot a final-round 65 without a single bogey to finish on 17-under for the week, but still ended up losing by three shots to an inspired Stenson.
"I knew that he would ultimately come through and win. I'm disappointed that it was at my expense".
Mickelson definitely felt as if the battle was like the Duel in the Sun between Tom Watson and Jack Nicklaus at Turnberry in 1977. By early in Sunday's round, he said "it was pretty obvious that it was just us".
In a way, maybe even a little more. "You played some great golf and obviously I'm delighted to come out on top this time, but thank you very much for a great fight". I played a bogey-free round of 65 on the final round of a major.
He would've been the oldest victor of the Open since 1867.
Mickelson, a five-time major victor, had never lost one like this. And I put in my best performance today. "And yet I got beat".
The greater the pressure, the better the golf until Stenson had broken one record, tied three others and won his first major.
He looked like he'd done it all before. "Even at the prize-giving ceremony he said "I haven't taken it in yet", that just shows how concentrated he was", said Jacklin.
Forty "is the new 30", he told Sky, and there was certainly something about the week for the older guard, with Mickelson, at 46, coming so close to being the oldest Open victor in almost 150 years.
That, along with 20 miles of Ayrshire coastline, might be all that separates two of the most compelling duels in 156 years of the British Open.
Just like Watson and Nicklaus before them, Stenson and Mickelson sprinted away from the field after 54 holes by playing the greatest golf on the grandest stage, the best you'll likely ever see.
Stenson's 20 under mark was an astounding 14 strokes better than third-place finisher J.B. Holmes.
"I was fortunate to watch every second of today's final round of the Open Championship, and I thought it was fantastic", Nicklaus tweeted.
"It was a great match, I knew he wasn't going to back down at any point, and in a way that makes it easier for myself".
Add in the loss of millions of dollars in disgraced financier Allen Stanford's Ponzi scheme in 2009, as well as some serious health problems - including one caused by a parasite picked up on holiday - and Stenson's recovery is all the more remarkable. Stenson's second shot rolled off the right side of the green, leaving him with a 50-foot putt up the ridge.
Mickelson, who beat runner-up Stenson in the 2013 Open at Muirfield, was generous in his praise.
That was the decisive blow.