O'Sullivan accused Carter of being "not a nice person" and in need of counselling after his opponent criticised his behaviour during the final at London's Alexandra Palace.
Carter accused the world number one of "snotting" - clearing his nose - "all over the floor".
"He (Carter) has got issues. He's got to go and sort his life out," O'Sullivan, nicknamed 'The Rocket', said in response to the claims.
"He's got to go and see a counsellor or something. He's got to deal with that because that isn't any good.
"I don't talk to him. I haven't spoken to him for 20 years. I played with him when he was a kid, shared a lot of stuff with him.
"For him to come out and trash talk me like that, everybody knows what he's like, he's got issues. Why has he got issues with me? I'm not having it. I don't care."
O'Sullivan, who had a run-in with Carter in 2018 when the two players 'shoulder-barged' each other during a match, also accused his opponent of being a nightmare to play against.
"He's a nightmare. To have to play snooker against someone like that is a nightmare. (He's) not a nice person, not a nice vibe that he leaves around the table," the seven-time world champion said.
Asked for a comment on O'Sullivan and Carter's latest stand-off on Tuesday, a World Snooker Tour spokesman said the comments "were under review."
