Chelsea had two players sent off and lost to Burnley 3-2 in the first match of its English Premier League title defence on Saturday
Burnley's win, their first at Chelsea since 1971, further blackened the mood around Stamford Bridge after a close season during which Conte has grown frustrated by his club's lack of transfer activity.
Conte was without the injured Eden Hazard and out-of-favour striker Diego Costa, while ?58 million ($75.5 million, 63.8 million euros) signing Morata started on the bench.
Liverpool were denied a winning start as Miguel Britos claimed a contentious stoppage-time leveller to earn Watford a 3-3 draw at Vicarage Road.
Watford twice went in front through Stefano Okaka and Abdoulaye Doucoure, but Liverpool equalised each time via Sadio Mane and Roberto Firmino, who then teed up new boy Mohamed Salah to put the visitors 3-2 up.
Watford and Liverpool shared six goals in a wildly entertaining match.
Liverpool boss J?rgen Klopp was furious that Miguel Britos (L) wasn?t ruled offside when the Watford defender poked home from on the goal-line after Richarlison?s shot was pushed onto the crossbar by Liverpool goalkeeper Simon Mignolet.