It was a fiesty affair at Stamford Bridge, with referee Kevin Friend dishing out five yellow cards in the first half and seven across the 90 minutes.
The managers clashed with a war of words during the game, but neither was willing to shed much light on the altercation after the match.
When asked if there was a problem between the two, Sarri told Sky Sports: "No, I think it was a normal discussion on the pitch.
"At the end of the match, there wasn't a problem between me and Marco."
The Everton boss similarly downplayed the encounter. When asked what was said on the touchline, Silva replied: "Normal things.
"The players are playing and you are playing outside as well. There is big respect between us.
"He is a fantastic coach, but he wants to win. I want the same thing as well. It is normal.
"At the end, we spoke and everything is ok."
Although it was not the result he wanted, Sarri made history on Sunday by becoming the first Premier League manager to go unbeaten in his opening 12 games.
When asked about the achievement, Sarri said: "I am very, very proud about it.
"Of course, I have to say thank you to the club because they gave me a very strong squad and I have to say thank you to the players and of course to my staff.
"I am really very happy with the record, but I'd prefer three points today."
After the international break they will face Tottenham at Wembley, and will host City in a huge clash on December 8.