Djokovic, Coric, Grigor Dimitrov and Viktor Troicki all tested positive during the event in Serbia and Croatia, which was later abandoned.
"I read what he wrote, but I simply don't care because he likes to be a general after a battle," Coric told Croatia's Jutarnji List newspaper.
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"If someone else was teaching lessons I would have understood, but Kyrgios ... it's somehow not realistic."
Kyrgios had also criticised Alexander Zverev after a video of the German player dancing at a crowded club emerged online despite the world number seven pledging he would self-isolate following his appearance at the Adria Tour.
"I agree that was not good, Zverev acted badly," said Coric. "But I don't see the need to criticise fellow players in such a way. I wouldn't do it, but again — it's Kyrgios."
Kyrgios shot back at Coric, saying he "should care" about his comments.
"Do you have rocks in your head?" Kyrgios said on Twitter. "Again, you can stand up for your mates, I'm just trying to hold them accountable. They are tennis players, they aren't special."

Dimitrov: Tough road back

Dimitrov has spoken of the problems he has faced since contracting coronavirus.
The Bulgarian returned to action at the weekend, playing in Patrick Mouratoglou's Ultimate Tennis Showdown. He did not enjoy much success - losing to Richard Gasquet and then Feliciano Lopez - but he was not too disappointed.
"I came in honestly with no expectations,” Dimitrov told Tennis Majors. “I haven’t practiced for that long. I’m just trying to focus on the format and enjoy it. Clearly I’m not ready to compete at the highest level right now. The movement is getting better; everything is kind of going in the right direction but it’s still not easy to recover. I’m far (from my best level) for sure. I haven’t played tennis in over a month. The virus was hard on me. I stayed home for about a month. It’s a tough road back.”

Croatia's Borna Coric, Bulgaria's Grigor Dimitrov, Serbia's Novak Djokovic and Germany's Alexander Zverev pose for a group photograph ahead of an exhibition basketball match in Zadar

Image credit: Getty Images

Dimitrov was so ill previously that he was unable to practise, and he reported breathing difficulties as well as fatigue.
"To be honest I’m lucky to be on the court right now," he admitted. "I don’t take each day for granted. I really appreciate being here. It’s so nice that during time off you can come out and play with your competitors.”
He added: "One day I feel really well and I have about four hours to be out [on court]. But then all of a sudden I need to completely shut down, take a nap or just rest. So I have to go through that process as much as possible. Hopefully I’m going to recover fully.”
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