Chelsea remain 11 points behind leaders Manchester City after labouring to victory against the Swans through Antonio Rudiger’s first league goal.
Conte was dismissed from the touchline for the first time in his Chelsea career by Swarbrick moments before half-time after furiously protesting the award of a Swansea goal kick and questioning the visitors for time wasting.
“It’s right to apologise for what happened during the game,” Conte said.
“During the game, in the first half, I saw that Swansea was wasting time. I said this a few times to the fourth official.
“At the same time, I didn’t see something change. I was frustrated for this situation. I tried to tell again, but then the referee took this decision.
“I apologise for this. I was frustrated. For sure I made a mistake. During the game, I suffer. With my players, I suffer. It’s a pity.”
The Football Association will await Swarbrick’s report before determining if additional disciplinary action against Conte is necessary, but it appears unlikely after the officials accepted his apology.
Conte watched the second half in the dressing room, but still in his animated way.
“I suffered in the same way,” he added.
“To watch the game on the video (screen) and then to not have the possibility to communicate with your players. It’s very strange. It’s very tough for me.”
Chelsea struggled to kill off their poor opponents, who did not have a shot until the 66th minute and did not have an effort on target at all.
Conte, though, praised his side for their positional discipline.
He added: “My players never lost their balance, they played an intelligent game. We must be very good also to win this type of game.”
Conte again said Chelsea must focus on themselves after City claimed a late win over Southampton to maintain their commanding lead.
And the Italian expressed hope David Luiz’s knee injury would not lead to a lengthy absence after the defender sat out the game.
“I hope to not lose him for a lot of time,” he said.
It was a fourth straight game when Swansea have failed to score.
Swans boss Paul Clement said: “We’re not creating many chances and we’re not scoring many goals. We’ve scored seven goals in 14 games and that’s going to make things very tough.
“We did OK tonight. We did frustrate Chelsea the way we set up.
“Most disappointing for me was the nature of the goal. There were players that had their backs turned, they weren’t in the right position.
“We’re so desperate for points at the moment and on another night, a little bit more quality in the final third we might get something.”
Renato Sanches, on loan from Bayern Munich, was replaced at half-time.
Clement said: “He wasn’t injured. He had a poor half. I don’t think in any of the games he’s played this year he’s showed the talent he has. He’s a player struggling for confidence, struggling for form.”