Johnson was the hot favourite after establishing a four-stroke cushion on Friday, and while he came back to the field in difficult conditions the following day he started the final round in a four-way tie for the lead and still, in many minds, the man to beat at Shinnecock Hills.
However, Johnson's final round of 70 saw him finish two shots behind Koepka in third place at three-over-par 283.
The 2016 champion had nothing to say to the media after his round but Koepka had high praise for his Florida neighbour.
"In my mind, he's probably one of the most talented guys to ever play the game," Koepka said.
"The attitude, the work ethic, everything that he brings to it, in my book he will, when he's done, probably go down as one of the best of all time.
"He's going to win another (major), we all know that. How many more he wins, we don't know."
Johnson, 33, did not miss a green until the seventh hole but failed to one-putt any of them.
A four-foot miss at the seventh, where he made his first bogey of the day, did not quite signal the end of the American's chances but the warning signs were there.
It could not have helped his confidence watching playing partner Koepka putt with poise and precision.
As the round progressed, Johnson spent longer and longer trying to read his putts. A 12-foot birdie at the last was too little, too late.
(Editing by Peter Rutherford)
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