Beasley reportedly said the ailment ached during the wild-card and divisional rounds but didn't bother him during Sunday's AFC championship loss to the Kansas City Chiefs.
"There was no way I was gonna miss a playoff game," the Bills receiver said, according to NFL Network's Kim Jones.
Beasley added, "Take a few meds and suck it up."
The 31-year-old wideout missed Buffalo's regular-season finale with a knee injury before returning to play in all three of the club's postseason games. Beasley caught 14 passes for 145 yards during the playoffs, including a team-leading 88 yards against the Chiefs.
With an offense that ranked second in scoring, the Bills' quest for a Super Bowl appearance ended with a 38-24 loss to the league's defending champs. Buffalo's appearance in the conference title game was its first in 17 years, and Beasley believes the franchise won't have to wait as long for a second go-around.
"(The Chiefs) just played better than us yesterday. They beat us. We didn't play our best ball, but they took it to us. They aren't going anywhere, but we aren't, either," Beasley said, according to team reporter Sal Capaccio.
Beasley enjoyed a career year in 2020, setting personal bests in receptions (82) and receiving yards (967).