Bjerregaard posted an 11 on the par-5 18th hole at Pebble Beach during the first round. USGA officials originally recorded his score as a 13.
The USGA's scoring change Thursday prevented Bjerregaard from registering the third-worst score on one hole in a major championship in the last 20 years.
"It's tough. It kind of ruins it all for me," Bjerregaard told reporters. "It's a course where you have to limit your mistakes. You can't afford to be making 11s."
Bjerregaard needed four tee shots to hit the fairway after slamming the first two into the water and a third out of bounds. After hitting the middle of the fairway on his fourth tee shot, the 27-year-old Dane took two more shots and two-putted for an 11.
Ray Ainsley holds the record for the highest single-hole score in U.S. Open history, carding a 19 on the par-4 16th hole at Cherry Hills in 1938.
Billy Casper matched Daly for the worst one-hole score in a major throughout the last 20 years after he made a 14 on the 16th hole at the 2005 Masters. Sergio Garcia carded a 13 on the 15th hole in the 2018 Masters.