Having scored 20 Premier League goals last season, there aren't many strikers that can replicate the scoring form of Costa - but Morata has certainly taken Chelsea to another level and at this rate, he is set to surpass his predecessors scoring achievements.
Conte had words of thanks for the travelling Chelsea supporters...
And the hosts' new backline was caught out nearly immediately, with a long ball from Cesar Azpilicueta - deputising as captain with Gary Cahill on the bench - allowing Morata to race clear and beat Jack Butland with a simple finish. "This game is very hard - I remember last season". I am pleased with his performance and the performance of the team.
"Now it is very important to prepare. Michy did the same versus Forest".
Having scored his first three goals for his new club with his head, the £60 million ($81 million, R525 crore) signing from Real Madrid netted all three goals with his feet in the Potteries and he might have added to his total from two late chances.
"It's great he got a hat-trick".
Morata marked his Premier League debut with a goal in a 3-2 defeat to Burnley.
The Belgium worldwide converted a rebound in the first half to give Jose Mourinho's side a fifth win in six Premier League games and keep pace with Manchester City at the top of the table.
And just like Costa, Morata was back in his own area heading balls to safety when required.
Chelsea and Manchester City were the biggest winners on a goal-packed day of Premier League action, while there were also victories for Tottenham, Manchester United, Watford, Everton and Liverpool.
Morata has so far proved to be an able successor and Conte said: " I think Alvaro played very well and he took his goals very well, which for a striker is very important.
Hughes said: "When you go up against a side of the quality of Chelsea, or any side in fairness, you've got to make sure you don't have catastrophic defensive moments and we had at least three, which is always going to make it hard".