The Australian struggled throughout the match with pain in his left knee, eventually falling 6-3, 6-4 on Friday in the third round of the Murray River Open.
"I can't serve without pain ... when I land it feels unstable," he told a trainer between the first and second sets. "I'll probably just play one more game. I'm serving at like 170 [km/h] instead of 220."
After having his serve broken at 4-4 in the second set, Kyrgios let out a series of expletives, smashed his racket and threw it into the empty stands.
He was handed multiple warnings by the chair umpire for his behavior, including a point penalty for unsportsmanlike conduct.
Coric was one of the players who tested positive to COVID-19 last June at the Adria Tour event organized by Novak Djokovic, whom Kyrgios later labeled "boneheaded" for going ahead with the exhibition tournament.
Kyrgios' defeat left three Australians still vying for spots in the Murray River Open's last eight.