A fired-up Costa had given the visitors a first-half lead and salvaged a point with a thumping overhead kick after Gylfi Sigurdsson, with a penalty, and Leroy Fer had capitalised on defensive howlers to instigate a quickfire turnaround.
The draw represented Chelsea’s first dropped points of the season, and kept the Blues second in the table, two points adrift of leaders Manchester City. Swansea moved to 13th.
Costa was his usual bullish self at the Liberty Stadium and was booked for a clumsy challenge on Federico Fernandez, while he also clashed with fellow centre-half Jordi Amat. Conte felt Costa was harshly treated and far from the villain of the piece.
“After every game I am asked about the patience of Diego Costa,” said Conte. “I am very happy with his patience. From the first minute until the 94th, he took a lot of kicks and it’s incredible that the defender didn’t finish before the end of the match.
“It’s difficult to talk about the game because today we lost two points. We were dominating the game and creating a lot of chances to score the second goal.
“It’s a pity because when you’re in a position to kill the game you must kill the game. We know that we lost two points.”
Chelsea opened the scoring on 18 minutes following two counts of calamitous defending from Fernandez, which ended with Oscar squaring the ball for Costa to decisively curl an effort beyond Swansea goalkeeper Lukasz Fabianski.
The Blues appeared in complete control until shortly before the hour mark when Thibaut Courtois misjudged an arced cross from Modou Barrow and could only foul Sigurdsson as he tried to retrieve the situation.
Sigurdsson netted the resulting spot-kick to become Swansea’s all-time leading Premier League goalscorer with 26, and just two minutes and 10 seconds later the hosts were ahead.
Fer appeared to foul Chelsea defender Gary Cahill as he challenged him from behind, but with play waved on by referee Andre Mariner, the former QPR midfielder managed to bundle the ball through Courtois.
But the pugnacious Spaniard came to Chelsea’s rescue on 81 minutes. As Branislav Ivanovic’s blocked shot looped into the air, Costa crashed an acrobatic effort past Fabianski. Only five players – Andy Cole, Alan Shearer, Fernando Torres, Kevin Phillips and Ruud van Nistlerooy have reached 35 Premier League goals in fewer appearances than Costa’s 58.