Morata scored twice in victory over Crystal Palace.
The goals took his tally to six this season after a difficult first campaign in English football.
“Obviously the goals help a lot because we that gives him more confidence, he has been playing well, finding opportunities," Azpilicueta said.
“Sometimes the ball does not go in. But I'm happy with his work, with his progress, we know that last season was a tough one for him, so always he is very important player for us."