Conte was sent to the stands in the closing stages of the first half by referee Neil Swarbrick after the Italian had aggressively confronted fourth official Lee Mason.
The Italian, who later revealed he had apologised to Mason and explained the reason for his anger, opted against appealing the charge and will be satisfied will avoiding a touchline ban.
“After the game it is right to apologise for what happened during the game,” Conte said.
“In the first half Swansea were wasting time. I said this a few times to the fourth official, but I didn’t see anything change. I was frustrated because of this situation and tried to say again. The referee took this decision but I apologise. I made a mistake.”
Conte witnessed his team draw with Atletico Madrid in the Champions League on Tuesday night to secure passage to the knockout rounds as group winner ahead of Roma.
The draw for the Last 16 will take place next week, with the reigning English champions currently able to get Basel, Bayern Munich, Juventus or Real Madrid. Three more teams, which could include Shakhtar Donetsk or Napoli, and Porto or RB Leipzig, among others will be added.
In the Premier League, meanwhile, Chelsea face a London derby against West Ham in Saturday’s early kickoff, followed by a trip to Huddersfield three days later.