The defending champions were stunned on Saturday as an own goal by Cesar Azpilicueta and a Wilfried Zaha strike handed them back-to-back defeats for the first time this season.
After the match Conte called for unity within the club to get out of their bad run.
But privately the Italian is furious with his players for their performance at Selhurst Park.
According to the Telegraph, Conte accused his Chelsea squad of being complacent against Palace and claimed they will struggle this season without an improvement.
Conte’s frustration is also understood to stem from his mounting injury problems.
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Chelsea faced Palace with the injured Alvaro Morata, N’Golo Kante and Danny Drinkwater.
Victor Moses was then forced off with a hamstring injury and is expected to be out for four weeks.
Michy Batshuayi’s Chelsea future is also in doubt after he failed to make an impact against Palace.
The Telegraph report says Chelsea are likely to look for another striker who can provide better back-up service to Morata.
Chelsea were linked with Fernando Llorente in the summer until he opted to join Tottenham instead.
Moves for Christian Benteke, Jamie Vardy were also considered while Red Star Belgrade striker Richmond Boakye will be watched by scouts against Arsenal this week.