The 6-4 4-6 6-3 loss marks the first time the 19-year-old has been defeated in a completed match at a grand slam, with her only previous loss coming when she pulled out with breathing difficulties against Ajla Tomljanovic in the fourth round of Wimbledon.
That proved a valuable experience and surely this will, as well, with the US Open champion again showing her competitive qualities and giving herself a chance when it appeared a lost cause.
Eurosport announced that Raducanu's first-round win over Sloane Stephens on Tuesday generated the channel's biggest audience in the UK for five years, and victory was clearly a big relief for the teenager after a tricky few months trying to adjust to her new status.
This was another new situation for Raducanu, who was the big favourite for a grand slam match for the first time against the world number 98, but she looked calm initially, rattling through the first three games.
Kovinic dug in, though, and, it soon became clear that all was not well with Raducanu. She called the trainer after five games and took a lengthy medical time-out for treatment to her right hand.
With the 17th seed clearly hampered on her forehand side, Kovinic made it five games in a row to lead 5-3 and, although Raducanu broke serve in the next game, the Montenegrin took the set.
By the start of the second set, Raducanu was chopping under virtually all her forehands, which at least had the effect of unsettling Kovinic, who promptly dropped serve.
One of Raducanu's key strengths, despite her inexperience, is her competitive nous, and she made life uncomfortable for Kovinic, consistently pulling her into the net and passing or lobbing her.
The Montenegrin looked like she had got a grip on proceedings when she broke back for 4-4 but Raducanu, who seemed to be enjoying the challenge despite the pain, broke again and managed to serve out the set.
It was clear how much the blister was bothering her as she winced during further treatment but she was able to hit out more early in the decider.
Kovinic got the better of a series of tight games, though, with the match briefly disrupted while a seagull flew circuits of Margaret Court Arena.
Raducanu tried to find a way back but it was Kovinic who prevailed to became the first player from Montenegro to make it to the third round of a slam.