Morata is now preparing for his return to Spain for their Champions League clash at Atletico Madrid.
Courtois said: "We know Alvaro is a top striker, we know he has ability and I am very happy for him that he scored a hat-trick. It's good for him and all of the team, Stoke away is a very hard game.
"But it's not just his hat-trick against Stoke, he has been scoring from the beginning. He is feeling good, strikers always do when they're scoring. He has scored a few important ones for us already."
But Courtois expects Morata to face a hostile reception from the Atletico fans, given he used to play for their fierce city rivals.
"He will get a different reception to me!" Courtois said. "Alvaro played a lot of games against Atletico, but for him it will be a big game against his rival of all time."