Morata signed for Chelsea this summer and has been on fire since arriving in London.
The Spain star has scored eight Premier League goals this term and one in the Champions League.
He replaced Costa as Chelsea’s main man and former Blues star Poyet thinks he can be important than he was if he sticks around for long enough.
Poyet told BetStars: “I think he has all the attributes, when a player [like Morata] plays for the teams that he’s played in early in his career, he will show you that he’s got all the qualities.
“I think the most important thing for Morata, and this is key, is to want to be the main striker for four or five years.
“Forget about changing, forget about being the super sub or whatever – be in the team that is best for you, being the main striker, playing week in week out and staying there for four or five years.”
Costa left under a cloud in the summer after a fallout with Conte.
He has signed for Atletico Madrid and can play again from January.
The La Liga club are under transfer embargo and cannot register new players until the turn of the year.
Costa helped Chelsea to two league titles in three seasons but fell out with Conte in January last year.
He refused to return from Brazil in the summer after being told was no longer wanted and was fined for failing to train with the side.
Morata meanwhile has taken to life in London with far less fuss.
