He was just four-hundredths of a second off the world record (12.80), set by Aries Merritt in 2012 at a Diamond League event in Brussels, Belgium.
"I thought I could break the record today," Allen told reporters after the race, according to NBC Sports Philadelphia. "Clean up a few things, and four-hundredths of a second is four-thousandths of a second per hurdle, which is so small. Going to have to wait for another race."
Grant Holloway, the silver medalist in the 110-meter hurdles at the Tokyo Olympics, finished second to Allen on Sunday with a time of 13.06. Holloway holds the second-fastest time ever at 12.81, which he ran in a semifinal heat at the Olympic track and field trials last year.
Allen finished fourth last year (13.21) and fifth in 2016 (13.31) in the 110-meter hurdles at the past two Olympics.
The 27-year-old Allen, a former Oregon wideout, signed a three-year contract with the Eagles in April. He hasn't played football since 2016, when he was with the Ducks. Allen caught the attention of scouts at Oregon's pro day in April when he ran an unofficial 4.35-second 40-yard dash.
He told reporters at Oregon's pro day that he planned to compete at the the USA Track & Field Outdoor Championships, which will be held later this month, and the World Athletics Championships in July, before turning his attention to football.
ESPN's Tim McManus contributed to this report.