Conte lost his cool during the first half of the clash against Paul Clement's side at Stamford Bridge, with fourth official Lee Mason taking the brunt of the Italian's anger over what he perceived to be blatant time-wasting from the visitors.
The Chelsea boss had to watch the remainder of the game from the dressing room as Antonio Rudiger scored the only goal to give the Blues a deserved but not overly convincing victory, and afterwards he saw fit to apologise to Mason and referee Neil Swarbrick, who banished him from the touchline.
"After the game I think it's right to apologise," Conte said in his press conference, per Football.London. "I saw that Swansea were wasting time. I said this to the fourth official. I was frustrated. I tried to tell again. Then the referee took this decision. I apologise for this.
"I was frustrated for this situation. I tried to tell again and the referee reacted to this situation. For this, I apologise, for sure I made a mistake but I suffer during the game. I suffer with my players, it is a pity.
"I suffered in the same way, also in the changing room, also on the video. I didn't have the possibility to communicate with my players, it was very strange."
Conte will likely receive a touchline ban for his antics against Swansea and could receive a suspension before Chelsea's lunchtime clash against Newcastle United on Saturday. Asked if he was worried about a ban, Conte said: "I told you what happened. I shouted this after a few times I saw the same concept."
Conte is not the only Chelsea star who could miss Newcastle's visit to Stamford Bridge; defender David Luiz will almost certainly sit out of the clash with the Magpies due to a knee injury that saw him miss the clash with Swansea. Conte was rather pessimistic over the Brazilian's chances of facing Rafa Benitez's side, who stopped a run of four consecutive defeats with a 2-2 draw against managerless West Bromwich Albion on Tuesday.
"Now it is very difficult [for Luiz]," Conte said. "He had liquid in his knee and we have to assess his recovery on the time, I hope to not lose him for a lot of time and I need to have all my players."