Hazard, meanwhile, made his first Chelsea start of the season in the 5-1 EFL Cup win over Nottingham Forest on Wednesday after breaking his ankle in June and Conte now considers his recovery to be complete.
Stoke stayed in the game until Morata finished them off with goals in the 77th and 82nd minutes, first dinking the ball over Butland and then tapping in to take his season's tally to six.
"If you look at Costa, he was brilliant at taking it up to the edge, then stepping back, and it affected opposition teams".
Zouma has impressed for Stoke so far this summer after moving to the Britannia Stadium for the season.
Moments after collecting a yellow card early in the second half following a challenge on Joe Allen, Chelsea's Marcos Alonso provoked loud appeals for a red from Stoke fans as he brought down Mame Diouf. Mark Hughes, meanwhile, added Peter Crouch to the mix and the veteran striker made an instant impression, setting up a stretching Diouf to fire over.
Stoke continued to press, with Fletcher's poor afternoon continuing as he somehow failed to convert Shaqiri's deep free-kick from six yards.
The Spain global bagged a hat-trick as the Blues battered Stoke 4-0 at the Bet365 Stadium.
Morata was mainly drafted in as a replacement for Diego Costa, who finally secured a move back to Atletico Madrid on Thursday.
However, Pedro Rodriguez extended the lead to 2-0 for the Blues in the 30th minute with a right footed strike from outside the box.