Upon the final whistle, Mourinho approached his Italian counterpart, shook his hand and reportedly said to him: "You don't wind up the crowd at 4-0. You do it at 1-0. It's humiliating."
In a post-match interview, Conte was asked for his take on the row and not only defended his actions, but also made a subtle dig at United's manager.
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"I was a football player, so I know how to behave on the pitch," he said, per the Mirror.
"There were United fans who kept singing, while ours were in silence after a great performance from my team. I wanted to call the crowd to applaud the players, which seems normal enough to me.
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"I have great respect for everyone. Nothing happened with Jose, especially as my behaviour seemed normal. I didn't make fun of or humiliate anyone, as I always demand respect."
The dust has now settled on Mourinho and Conte's coming together, but that hasn't stopped Chelsea winger Pedro from having his say.
Speaking to Spanish radio station Cadena Ser, brought to our attention by 101 Great Goals, the 29-year-old defended his manager and berated Mourinho.
"Mourinho's reaction was out of context," he said. "Conte was not making humiliating gestures or jeering.
"He was only cheering on the fans because we had played a great game and he wanted the supporters to sing in order to help us finish the game in the best possible way.
"I don't know if Mourinho considered it a lack of respect or a provocation but that was not Conte’s intention. Conte just wanted to thank the fans for the support. The fans were incredible.
"There was a touchline spat between the two coaches at the end of the game but I reiterate that there was no bad intention from Conte.
"We all know how Mourinho is and the comments he makes. Perhaps the defeat was tough on him."
It was Pedro's goal within 30 seconds that set the tone at the Bridge, latching on to Marcos Alonso's ball over the top before rounding David de Gea and firing home.
Gary Cahill soon added a second from a corner, with Eden Hazard making it 3-0 after half-time following some lovely build-up play in the centre of the park.
A fourth from N'Golo Kante capped an historic afternoon for Chelsea. The Frenchman fooled Chris Smalling with a fake shot before slotting past De Gea and into the bottom-left corner.