The Premier League champions got the defence of their title off to a nightmare start at Stamford Bridge as skipper Gary Cahill saw red with just 14 minutes on the clock, allowing Sean Dyche's men to run into an unlikely 3-0 lead by the break.
Record signing Alvaro Morata and David Luiz did manage to restore some dignity by pulling the scoreline back to 3-2 come the final whistle, although Conte was delivered another headache when Cesc Fabregas also received his marching orders nine minutes from time.
"The sending off of Cahill was a key moment, because to play the rest of the game with 10 and then nine men is not easy," Conte told reporters afterwards. "In recent games we have finished with nine or 10 men. I have to try to adapt a new system and to anticipate playing with nine or 10 men in the next game. I don't want to comment on the referee, absolutely not.
"We tried until the end to reach a good result against Burnley - it was a pity because our fight in the second half was very good.
"But our first half we kept losing our heads - after the red card we lost our heads, conceded two goals and then it's very difficult to change the final result."
Next up for the Blues, who have now lost their last three competitive matches, is a tough trip to Tottenham Hotspur at Wembley next weekend.