David Luiz accused Burnley of playing "anti-football" after Chelsea's top four hopes were dented on Monday night.
The Clarets led through Jeff Hendrick's early volley before Ngolo Kante and Gonzalo Higuain turned the tide in favour of the hosts.
But Ashley Barnes scrambled home to level and stern rearguard action helped the visitors to Stamford Bridge a point that should secure their Premier League safety.
Burnley's efforts included frequent attempts to slow the game down with goalkeeper Tom Heaton booked for time-wasting in the 31st minute.
"We tried everything to win the game," Luiz said. "It's difficult when you play against a team who have two chances and score two goals and didn't want to play the game.
"It's anti-football. Losing time [time wasting] all the time, especially when you have the ball. Their players went to the floor and stopped the game."
Blues assistant manager Gianfranco Zola didn't think referee Kevin Friend added enough time on to compensate for the Clarets' tactics.
"Five minutes injury time wasn't enough to compensate," he said. "We expected it to be a tough game.
"We didn't expect so much time-wasting. We expected the referee to give more extra time. That's why we're very unhappy."
Maurizio Sarri refused to talk to the media after the match incensed at being sent off late on and claiming he was abused by the visiting coaching team.
Chelsea defender Antonio Rudiger and Burnley goalkeeping coach Billy Mercer had to be separated by the officials at the final whistle, as a gripping encounter ended in ugly touchline scenes at Stamford Bridge.
Luiz and Ashley Westwood then clashed as the teams left the field, and that after Gonzalo Higuain had thrown a bottle into the dugout in a petulant response to being replaced late on.
To make the night worse for Chelsea, England forward Callum Hudson-Odoi later confirmed on social media that he will miss the rest of the season with a ruptured Achilles tendon.
Asked if Chelsea will contact the FA over Sarri's frustrations, Zola said: "I think there will be a follow (up) on that. Maurizio felt very unhappy.
"We understand it's a football game. You say words because of the adrenaline, but he wasn't particularly happy.
"If Maurizio said that, probably it's something that could have been avoided."
