Only two other men have returned 62s at a major, Rickie Fowler, also in the first round at the 2023 US Open and Branden Grace, in the third round at the 2017 Open Championship at Royal Birkdale.
"I'll take a 62 in any major any day," Schauffele said.
"Not winning makes you want to win more, as weird as that is.
"For me, at least, I react to it, and I want it more and more and more, and it makes me want to work harder and harder and harder.
"The top feels far away, and I feel like I have a lot of work to do."
Lurking four off the pace on five-under are red hot world number two McIlroy and Scotsman Robert MacIntyre.
McIlroy, coming off back-to-back PGA Tour wins, carried that momentum into the first round. He rolled in a six-footer for a birdie on his opening hole, the par five 10th, then picked up a second at the 13th to briefly join a crowd at the top of the leaderboard.
But the Northern Irishman, who announced on Monday that he had filed for divorce, stalled after the early burst. He took a bogey at the 17th before hitting his stride again after the turn by carding four birdies, including three straight from the fifth coming home.
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"Not a pretty 66," summed up McIlroy, who won the last of his four majors in 2014 on the same Valhalla layout. "I sort of felt like it was pretty scrappy for the most part.
"I thought I got a lot out of my game today.
"Not really happy with how I played but at least happy with the score."
Defending champion and LIV Golf standard bearer Brooks Koepka, bidding to become the tournament's first repeat winner since he retained the title in 2019, looked a threat to add a fourth Wanamaker trophy to his collection after returning a four-under 67 highlighted by an eagle, birdie, par finish.
Tiger Woods, who collected one of his 15 major titles at Valhalla in 2000 with a play-off win over Bob May, opened with a one-over 72 but lamented a sloppy bogey, bogey finish to his day.
For Woods, this is his first event since the Masters. Last month the injury-ravaged golfer had earned a tournament-record 24th consecutive made cut at Augusta National and finished last among those who played the weekend.
"It's just that I just don't play a whole lot of competitive rounds," said Woods. "I haven't played since the Masters.
"So it's a little bit different than being at home and playing a flat Florida course."
New dad Scottie Scheffler, bidding for a fifth win in his last six starts, was just getting his round underway going out in the late wave.
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