The former world No.13, playing his first ATP Tour match since March and his seventh in three years, couldn't gain a foothold in 6-3 6-4 loss in 66 minutes on Tuesday.
Coming back after multiple knee and wrist surgeries, Kyrgios had two loose service games to blame in the loss that came after a handful of exhibition matches late last year and a doubles win in Brisbane on Sunday.
Kyrgios overplayed a drop shot, then missed a forehand volley to drop serve at 3-4 in the first set and then, after holding comfortably to reach 4-4 in the second, again gave up the break with a series of tardy points.
World No.58 Kovacevic produced 27 winners to Kyrgios's 10 and only lost one point when he landed his first serve.
A relaxed Kyrgios threw in an underarm serve and was happily chatting to his brother, who was sitting three rows behind him, in between games.
But Kovacevic wasn't fazed as he made his way through to the second round.
"A tough one to approach, you don't know what you're going to get with Nick, whether he's healthy or not," Kovacevic said.
"And tough to scout him recently, because he hasn't been on Tour for a while and playing serious matches.
"I just knew I had to be pretty locked in."Â
Yet to hear if he'll earn a wildcard for this month's Australian Open, world No.670 Kyrgios is due to play at the Kooyong Classic next week but has said his immediate playing future is unknown.
He will remain in Brisbane for now though, into the second round of the doubles alongside Thanasi Kokkinakis.
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