Morata joined the west London club from Real Madrid in the summer transfer window and he has now scored six goals in six Premier League appearances for Conte's men.
"I am pleased for his performance and pleased for the performance of the team".
"Now he is involved totally in our style of football and our idea and he is very strong", Conte said after the win. It means we create chances for our strikers.
Morata had previously asked Chelsea's fans not to sing the song about him and they responded by dreaming up a different chant in his honour.
On the half-hour mark, a dominant Chelsea made it 2-0 after Stoke captain Darren Fletcher's attempted chest pass back to goal instead set up Pedro, with the winger making the most of the gift and firing past Jack Butland. It is not easy to win away games against Stoke, this game is always hard. "This game is always hard", added Conte, whose side trail leaders Manchester City and Manchester United by three points.
"I remember very well last season when we struggled a lot to win and we won at the end of the game".
"Now it's important to rest well and prepare for another game against Atletico Madrid which will be a big game for us".
Chelsea keeper Thibaut Courtois suffered an injury after falling heavily but played on.
Stoke manager Mark Hughes had no such comfort after he saw his side undone by terrible defensive errors, then reported his centre-back crisis could extend into next week's home game against Southampton. As you know, Hazard is very important for us.