The Chelsea manager was delighted that the 58-million-pound striker seems to be fully recovered after his first season, which was damaged by sharp spinal problems in December.
But he says he has to get even stronger mentally if he wants to play against Sergio Aguero, Mohamed Salah and Harry Kane – the shooters on some of Chelsea's main title rivals.
"I do not know if he can score as many as this – he's a bit fragile from a mental point of view," was Sarri's honest assessment of Morata. "But he is very young and I think he can improve – very fast.
"He certainly improved in the last month. Improvement of confidence, improvement of personality, also technically improved. He has a lot of physical and technical potential, so I think he can continue to improve.
"Now he can play more with the team. He has to play with his friends without thinking of goals. Goals are usually the result of teamwork. "
His two goals against Palace have netted four goals in their last four Premier League games – more than Morata have scored in the last 23.
While his current number of goals was a relief to the 26-year-old, he admits he should have had a hat-trick in the game.
When he tried to chop away Wayne Hennessey in injury time to lift the ball as high as the goalkeeper's fingertips.
"If you have a bad period, it takes a long time to recover," he said. "The last year has been difficult for me in many ways. You do not expect injury, but now I'm fine, it's nice to score.
"I could have achieved a hat-trick, so it was not the perfect day. But we will take the three points. We want to fight for the Premier League until the end. "
His opening goal on 32 minutes after Pedro's attempt at pass, on the second try after a block from a defender at Palace, apparently got him off to a good start.
However, David Luiz was guilty of watching the ball shortly after the break and allowed Andros Townsend to pick up James McArthur's pass and hit a low shot in the far corner of the Chelsea net.
Fortunately, Sarri had an ace in the shape of Eden Hazard up his sleeve. The doctors had decided that the Belgian star was not good enough for a full 90 minutes and the Chelsea coach had decided to keep him for the end instead of risking him from the start.
Only 91 seconds after the kickoff, his free kick jumped to Morata, who dropped his second goal from a tight angle. Five minutes later, Marcos Alonso's cross was lowered by Pedro 12 meters away.
"Today it was very important to have Eden on the bench," said Sarri. "I talked to the doctor yesterday and he said he was better, but he can not play for 90 minutes.
We were lucky. I think he could change our game in the first minute. But you know Hazard is Hazard. He can do that very often. "
However, Crystal Palace manager Roy Hodgson, who has now scored two points from the last 18 points, was denied the crucial free-kick in the front row.
"The foul is cheap," he said. "I do not think many managers would find a foul for this kind of challenge.
"We showed against Arsenal last week and a good performance today. We can only hope to give this kind of performance, and hope that happiness develops along our way.
"We were rarely outside the relegation zone last season, but finished eleventh. We missed opportunities, yes, and we do not have as many points as we should.
"But let's see where we are after 38 games."
CHELSEA (4-3-3): Arrizabalaga 6; Azpilicueta 6, Rudiger 7, Luiz 5, Alonso 6; Edge 7, Jorginho 6 (Fabregas 80), Barkley 5 (Kovacic 64, 6); Pedro 7, Morata 8, Willian 7 (Hazard 64, 6). Booked: Milivojevic. Finish: Morata 32, 65, Pedro 70. NEXT UP: BATE Borisov (a), Thursday, Europa League.
C PALACE (4-2-3-1): Hennessey 6, Wan Bissaka 6, Tomkins 6, Sakho 6, Van Aanholt 7; Kouyate 6, Milivojevic, 6, McArthur 7 (Schlupp 80); Townsend 6, Zaha 7, Meyer 6 (Ayew 71, 5). NEXT UP: Tottenham (h) Saturday, PL.
REFEREE: M Oliver (Northumberland)