With just five minutes to the break, Conte looked desperate to get his players in for a regroup but the reigning champions dropped further behind as Burnley grabbed a brilliant second in the 40th minute.
Chelsea improved after halftime.
Morata was signed for a reported fee rising to £70 million and could make his Premier League debut against the Clarets. However, disaster struck in the final minutes when Cesc Fabregas received a second yellow card to reduce the Blues to nine men.
It was definitely not the start to a title defence Chelsea fans would have expected as Burnley took a shock lead. With Eden Hazard, Tiemoue Bakayoko, and Pedro Rodriguez injured and Victor Moses suspended, Chelsea had a threadbare match-day 18.
"The red card [for Cahill] was the key moment", Conte told BBC Sport.
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When asked if Pawson got the big decisions right, Conte replied: "Mmm.I prefer to not comment on the referee's decision and performance".
Even though Chelsea have won 15 of their last 16 home games and scored at least three goals in the most recent four of those, finding the net could be more of a struggle on Saturday.
In contrast, Chelsea won all but two games at Stamford Bridge, a record second only to Tottenham Hotspur.
Conte kept his counsel on Chelsea's transfer business, with the summer window open until August 31.
Morata, who joined from Real Madrid for a reported initial fee of £58million, had only made two International Champions Cup appearances for Chelsea prior to last Sunday's encounter following a lengthy transfer saga.
"I admit it's a very important amount but I have the personality to play with calmness and continue my path".
Conte added: "We must focus on working very hard with these players". You don't know me very well and you can see in our pre-season and in every friendly games I have always played the best formation and it happened the same also today.