Conte's Tottenham controversially rescued a 2-2 draw against Tuchel's Chelsea at Stamford Bridge on Sunday afternoon amid furious scenes which saw both managers sent off in the London derby.
At the final whistle, the two squared up following their post-match handshake, with Tuchel blasting the Italian in his post-match press conference.
Discussing his red card, he said: "I thought when you shake hands you look into each other's eyes. Antonio (Conte) had other ideas. Another poor decision from the referee today."
The German - seemingly more unhappy with referee Anthony Taylor than Conte - went on to blast the official's decisions regarding the Tottenham goals, adding: "Both goals should not stand. Only one team deserved to win, that was us."
Conte responded, stating: "In my opinion it is better to talk about the game. I don't want to comment on the situation, if there is a problem that is between me and him (Tuchel) and not anyone else. The referee showed me the red card but he didn't understand the dynamic of what happened. It's okay, I have to accept it. It's not a big problem."