The Chelsea manager, who saw Blues skipper John Terry leave the Liberty Stadium on crutches, went on the attack after what he perceived was unfair treatment meted out to Diego Costa.
Following calamitous defending by Thibault Courtois and Gary Cahill, Costa had come to his team’s rescue with a spectacular late equaliser, which set up an exhilarating finale.
And Conte complained his Spanish international was the victim of a miscarriage of justice because no Swansea players were sent off despite Costa being “kicked from the first minute to the last minute” by his markers.
“After the game, the press always ask me about Diego Costa but from the first minute until the 94th minute he took a lot of kicks and it’s incredible that the defender finished the match,” Conte said.
As for the question of whether Costa is targeted, Conte added: “Yes. I think that the defenders know him and sometimes they try to provoke him. It is normal in football.
“Diego is a player with great passion and they try to provoke but this is football not only in England and not only with Diego but I think the referee must see and permit Diego Costa to play his football.”
Costa, who was booked for a foul on Leroy Fer, largely behaved himself despite being treated as a pantomime villain by the Swansea supporters.
“I am pleased because he showed me and his teammates that he has fantastic behaviour,” Conte said. “It was not easy.”
Costa did, though, make goalscoring look easy when he put Chelsea ahead in the 18th minute.
The former Atletico Madrid striker showed off his finishing prowess when he deftly side-footed home after being teed up by Oscar.
With new signing David Luiz on the bench, Chelsea dominated a one-sided game but Eden Hazard, Cesar Azpilicueta, Costa and Terry all wasted opportunities to put the game beyond Swansea.
Then Courtois misjudged a through-ball from substitute Madou Barrow and felled Gylfi Sigurdsson just inside the penalty box.
Referee Andre Marriner showed Courtois mercy by not sending him off but Sigurdsson was less forgiving and dispatched his spot-kick down the middle in the 59th minute.
Three minutes later, Leroy Fer caught Cahill dithering over a back pass to Courtois and the midfielder raced through before squeezing the ball beneath the goalkeeper.
Conte refused to blame Courtois for his role in Swansea’s equaliser but did accuse referee Andre Marriner of missing a foul by Fer on the England centre-back.
“For the second goal I think everyone can see that tackle on Cahill and I think that there is a great mistake by the referee,” Conte said. “But I also want say that this can happen to one side or the other.
Chelsea’s reaction was impressive but it was left to Costa to preserve his team’s unbeaten start when he beat the otherwise excellent Lukasz Fabianski with an overhead kick from eight yards in the 81st minute.
That set up a frantic finale which saw Fabianski again foil Costa with a brilliant save as Swansea held firm.
Conte remained upbeat afterwards. “We had a fantastic reaction after the second goal because the players showed they did not want to lose and tried to win until the end and for this reason I am pleased,” he continued.
Swansea manager, Franceso Guidolin, later admitted that he had apologised to Neil Taylor for replacing him with Barrow just before half-time.
“I apologised in the dressing room,” Guidolin said. “Neil is a clever guy and so I think he understands but I made a mistake.
“I say that because I could I should have waited three minutes but Mo was ready for five minutes before and I decided to do it in this way. It is the first time that I have done this in my career.”
Fabianski 8: Fernandez 6, Amat 7, Kingsley 6; Naughton 6, Ki 7, Cork 7, Fer 7, Taylor 6 (Barrow 44, 7); Sigurdsson 7 (Rangel 89); Llorente 5.
Nordfelt (g), Van der Hoorn, Fulton, Britton, Montero.
Courtois 5; Ivanovic 7, Cahill 5, Terry 7, Azpilicueta 7; Kante; 6 Willian 7 (Moses 77), Oscar 7 (Batshuayi 88) Matic 7 (Fabregas 76), Hazard 7; Diego Costa 9.
Begovic (g), David Luiz, Alonso, Pedro.