Morata joined Chelsea for £70million this summer after spending much of last season on the Real Madrid bench.
The Spain international has arrived to replace Diego Costa who, although he wasn’t sold in the transfer window, has been ostracised from the first team.
And Morata told newspaper El Pais he must justify his transfer fee at Stamford Bridge.
“Fate has given me a chance,” he said.
“It is true that I have made some good games, I have scored goals that have earned points.
“And now I find a team that has made a huge financial commitment for a Real Madrid substitute.
“They have given me everything. Conte is with me until the death.”
Morata scored and assisted a goal in his first league appearance for Chelsea, coming off the bench in the 3-2 loss to Burnley.
The 24-year-old also found the flag in last weekend’s 2-0 triumph over Everton.
Last term he scored 20 goals for Real, having rejoined his boyhood club after two successful years at Juventus.
Asked by El Pais why Chelsea are a good choice for the striker, he said: “The difference is that Chelsea’s game is based on me.
“When we play with three up front we face opponents who defend with a line of three, as in Italy.
“The centre-back follows me and the other two take the wide men, Willian or Pedro.”