The pair were both sent off at the end of a spicy 2-2 draw at Stamford Bridge in the Premier League.
The pair came together at the end of the match during a handshake with the Blues boss appearing to grab onto his opposite number, who didn't look him in the eyes.
They clashed during the match too with Conte booked for celebrating Tottenham's first equaliser of the game in the face of Tuchel.
The German then ran down the pitch, as Jose Mourinho famously did at Old Trafford, when Chelsea claimed a 2-1 lead through Reece James.
Harry Kane levelled the game in dying seconds leading to the fiery coming together at the final whistle.
But Adebayo Akinfenwa and Darren Ambrose told talkSPORT they liked seeing that passion between the managers, which they don't believe ended in violent conduct.
"This is what we want to see," said Akinfenwa joyfully. "This happens in the EFL all the time.
"From what I saw, they went in for a handshake and like you do, they would have said something and then they squared up. It didn't look like any punches were thrown or anything.
"It's a derby and you want to see passion and that. When people all come in it makes it look worse than it is.
"I actually like that.
"If they don't get on, they don't get on. Not everybody has to get on. Players do tackles and there are rivalries.
"It's a London derby," added Ambrose. "Thomas Tuchel and Chelsea have conceded a goal with the last kick, or head, of the game to get one point instead of three points.
"From what I see, it looks like Tuchel held onto his hand as they had their handshake and maybe [Conte] wasn't looking him in the eyes.
"This is heated. This is right at the end of the game, they are going to go in they are going to calm down, there might be a little fracas in the tunnel as well.
"It was heated but for me it wasn't the worst ending to a match I've ever seen."
And Akinfenwa reckons Conte's actions were fully understandable.
He added: "You lot have all been there where you have high-fived a player and when you've high-fived him or shook his hand you've let him know you're not really cool [with him] and that's what it looked like he did.
"They are both feisty characters. Conte is going to be like, 'what are you doing?'"
"Conte is just letting him know Spurs are here," chimed in Ambrose.
"[Chelsea] should have won that game, they dominated, but Spurs are still here."