But Sarri dismissed comparisons with Didier Drogba for the Spaniard.
He said after the 3-1 win: "Alvaro improved the last month. Improved for the confidence, improved for the personality, improved also from the technical point of view.
"Now he's able to play more with the team, I think. But I think, also, that Alvaro has a very great physical and technical potential, so I think he can improve more."
When then asked whether Morata shares physical attributes with Chelsea's legendary striker Didier Drogba, Sarri replied: "Physically, no. But Drogba was one of the best in the world for 15 years. But Alvaro is very fast.
"[He's] not in the first two or three steps, but if he has to run for 40 metres he's very fast. He's strong, so not like Drogba. He has great potential.
"He has to play for the team, with his mates, without thinking about goals. Goals are usually consequence of teamwork.
"He's a little bit fragile. From the mental point of view. But he's very young. I think he can improve, improve very fast."