Runner-up a record six times in his national championship, Mickelson will turn 47 during next year's U.S. Open at Erin Hills in Wisconsin and history suggests he is on the verge of battling a lost cause.
Nobody has won the U.S. Open at such an advanced age, with American Hale Irwin becoming the oldest champion at 45 in 1990.
Mickelson, a perennial fan favourite, failed to advance to the final 36 holes at Oakmont Country Club after carding a 73 in the delayed second round.
"I didn't score the way I would have liked to, but I enjoyed the challenge," he told reporters after posting a seven-over total of 147.
"It's a fun opportunity to really test yourself when a course is set up like this that will reward good shots and penalize severely poorly struck ones."
Mickelson, who celebrated his 46th birthday on Thursday, rued poor putting on daunting greens at Oakmont.
"I actually thought I played really well, except I let four or five par putts kind of slide, and all of a sudden I'd be two over and right in it," said the five-times major champion.
"You can't do that here because you don't have those birdie opportunities to offset it, offset those mistakes. I didn't have very many birdie opportunities.
"My irons, they don't feel bad, but they're just a fraction off. Instead of hitting it to 15 feet and giving myself chances, I'm 30 feet, 40 feet away and fighting just to make par."
Mickelson oozed confidence coming into this week, but was wary of allowing desired results to affect his performance at Oakmont.
"This is the tournament I want to win the most to complete the four majors, there's no question," said the Californian.
"But I have to put that out of my head and try to execute and be patient, not think about results.
"You start thinking about results, you'll never play your best golf ... but until I ultimately win this tournament, it will be my biggest thought, my biggest focus.
"I view those players that have won the four majors totally different than I view all the others."
Mickelson has won the Masters three times and the British Open and PGA Championship once each.
A U.S. Open win would put his name alongside Gene Sarazen, Ben Hogan, Gary Player, Jack Nicklaus and Tiger Woods on the career grand slam list.
(Editing by Andrew Both)
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