The World No 1 entered the week as the clear favourite to land the only missing major needed to become just the seventh man in history to achieve the feat, but an opening-round 72 at Shinnecock Hills immediately put him on the back foot.
Eight strokes adrift of first-round leader Wyndham Clark, Scheffler mounted a steady recovery with rounds of 68 and 69 to earn a Sunday pairing with the frontrunner. He remained in contention deep into the final round, closing to within three shots with five holes to play.
However, he was unable to sustain the charge down the stretch, bogeying the 14th before finishing with four straight pars and final-round 71. Scheffler ended the week on level par, four shots behind Clark, and will now have to wait at least another year for a chance at the career Grand Slam.
"It was good to be back in the arena," Scheffler said. "I felt like at times this year I was on the outside looking in. I felt like I had given up too many shots early in the week.
"This year I haven't had many 36-hole leads. I haven't had any 54-hole leads. This week will be another example where you could chalk it up to the first round.
"Wyndham went out late in the day on Thursday and shot six under to my two over in the morning - that's eight shots right there. I don't know exactly what it is.
"I've been pretty good in first rounds over the last few years, and for some reason, the sharpness just hasn't been there early in tournaments. I haven't had those leads that I've needed in order to win tournaments."
Clark was jeered by sections of the crowd during the final round of his wire-to-wire victory, with Scheffler suggesting his playing partner was subjected to “a bit much” from the gallery.
"The crowd was tough today," Scheffler said. "New Yorkers, they are tough people. There was a good turnout from the fans. You like seeing the fans cheer for you. I think sometimes it can get a little too much when balls are going off greens and you start hearing cheers.
"But at the end of the day, I can't control fan behaviour. Being in the arena is not for everybody: there have been crowds that have been for me in my career; there have been crowds that have been significantly against me in my career.
"I think it shows a lot about Wyndham, how he handled not only this golf course but I think the crowd today as well and is a well-deserving champion."