The champions had Gary Cahill sent off early on for a risky tackle and the Clarets made their numerical advantage count as they stormed into a 3-0 lead before half-time, with Sam Vokes netting twice and Stephen Ward also getting on the scoresheet.
But Burnley held on to claim a first win at Stamford Bridge since 1971, and leave Conte lamenting the early dismissal of Cahill for putting his side on the backfoot.
While accepting that his players had been affected by the situation, Conte pointed to how they have now received red cards in each of their last three games - including the FA Cup final and Community Shield against Arsenal - but stopped short of blaming his players for ill-discipline.
"They opened up the pitch even more when they had 10 men which put us on the back foot a bit. They could have bought six or seven new players but everyone is upping their game, so I think it's a fair comment no matter what".
He said: "I knew Conte loved me and I had talked to him many times".
"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 hard to change the final result".
Summer signings Antonio Rüdiger and Álvaro Morata are both expected to feature in Chelsea's starting lineup, though Antonio Conte's side will be without the injured Tiemoué Bakayoko and Eden Hazard, while Victor Moses is suspended.
"Honestly, I am pleased with the squad because we are working very well with the players, the commitment is incredible, better than last season", he said.
Lampard, who scored 147 times for the Blues in the top flight, feels Conte is the best possible man in charge of the club where he spent 13 hugely successful seasons. I am not anxious.
"[They have improved from last year] in the way they work in the training session".
Chelsea down to 9 men.
"In our pre-season, in every pre-season, I played our best formation and I did the same against Burnley".
"Today big decisions changed the outcome, quite obviously", the Burnley manager said.
"I don't think I need to adapt to the Premier League, but to my new coach".