Kyrgios, who is now ranked 670th, is aiming to build up his fitness so he can gain a wildcard for the Australian Open, which begins on 18 January in Melbourne, after suffering a string of serious injuries in recent years.
He appeared to clutch his elbow in discomfort during the match with 58th-ranked Kovacevic, while he won a point with one of his trademark underarm serves in the second set.
The loss will not help Kyrgios’ hopes of playing in his first Grand Slam since a first-round defeat by Britain’s Jacob Fearnley at his home tournment in 2025.
He has had multiple surgeries on his knee and wrist since reaching the final of Wimbledon in 2022 but said he is “still extremely happy and proud” of himself for making a comeback.
“I thought I was the best player in the world,” said Kyrgios as he reflected on his injury journey.
“After you have these surgeries, I guess they kind of pull you down and it’s like you don’t have that belief anymore. It’s sad in a way, but that’s just the reality.
“I guess the people out there, they think that you just go under the knife and come back, you sit on the couch until he recovers and you throw him back out there and he’s the same player. That’s just not how it is.”
Kyrgios is next in action on Wednesday in the men’s doubles with Australian partner Thanasi Kokkinakis, before taking part in the Kooyong Classic warm-up exhibition event in Melbourne next week.