Tuchel had already rowed with Conte on the touchline during the match and the pair’s exchanges got more heated after Tottenham's controversial equaliser, which saw the German refuse to let go of Conte’s hand after the customary post-match handshake.
It has led the duo being charged by the Football Association, but Tuchel on Friday followed Conte in playing down the prospect of any further animosity.
“Of course, we laugh! It is very important to laugh about ourselves," Tuchel said at Cobham Training Centre. "I was laughing in the dressing room. It was the heat of the match, for me, still not that bad. A handshake and too long, too heavy! I admit it.
"No harm was done. He’s from my side. He spoke Italian to me so I never know. We didn’t insult each other. I think the thing would have ended if there were not 20 people around us that make the thing look much worse than it was.
"You are right. If you have a reaction like this, you need to live with the reaction. Of course, I laughed about myself. I saw quite some (compilations). Everybody makes fun of me in the building as you can imagine but it’s okay!”
Tuchel also risks the wrath of the FA for his comments about referee Anthony Taylor and his Video Assistant Referee (VAR) Mike Dean.
Dean, who pens a column in the Times, admitted that he may have made a mistake not telling Taylor to review a hair-pulling incident on Marc Cucurella by Cristian Romero.
Tuchel has no sympathy for the referees, which whom he remains angry.
"I struggle a little bit to be fully impressed by the statement I have to say," he added. "It’s so clear and obvious, I cannot understand how a referee cannot make the decision that was the right decision.”
Tuchel is likely to hear news on Friday evening about the severity of his punishment following the various incidents at Stamford Bridge last weekend.