Bucs beat the Clever Boys 3-1 in the Telkom Knockout final at Durban's Moses Mabhida Stadium on Saturday night, but the match was marred by controversy when Tinkler and McCarthy clashed at halftime.
In a post-match interview, McCarthy said Tinkler was "lucky" he didn't slap him.
Said McCarthy: "Eric Tinkler thought we were still team-mates in the national side, I even forgot that we played together in the national team. He tried to be smart so I had to put him in his place because when you as a player are getting pushed around left, right and centre by the opposing coaches, then me, I must defend myself. He is lucky I didn't slap him."
Speaking to Football365.co.za, Tinkler has set the record straight and says McCarthy must be "professional" and let the matter rest.
"People are making a big thing out of something that don't deserve all the attention, you know," says the former South Africa international.
"What happened there was that at half-time Benni was having an argument with one of our players 'Zane' (Sipho) Mngomezulu. I tried to step in to try and separate them and Benni didn't like the fact that I touched him," Tinkler explains.
"He shoved me in the face and he swore at me. I swore at him and it didn't go any further than that. People are just making a big thing out of nothing," he says.
Tinkler is seemingly irked over McCarthy's utterances and hit back at Bafana's record scorer.
"Benni is being stupid about it; you know what I'm saying. That (that Benni could have slapped him) is being ridiculous. He wishes he could have slapped me! I don't wanna go into things like that. Obviously tempers were flaring at halftime you know and that's what you get. It is part of the game.
"People are gonna have banter on the field and you just have to be grown enough to accept it and move on or be more professional about it. Like I said he was having an argument with one of my players and I just tried to separate them and he just didn't like the fact that I touched him," Tinkler concludes.