The Spanish forward inspired the Blues to a win which took them above Liverpool into second spot in the Premier League table.
Morata has netted 14 times in 40 Premier League appearances since joining from Real Madrid for a then club record £60m in July 2017.
Asked after the match whether Morata can be the main striker at one of the main clubs in the world, Sarri told BBC Sport: “I don’t know. I think potentially he can.
“He has to improve more in personality and in confidence because sometimes he’s a little bit fragile.”
Hazard makes immediate impact on return
The headlines will be about Morata – the former Real Madrid and Juventus forward has now scored five Premier League goals plus another in the Europa League this season.
Yet the return of Eden Hazard added much needed energy and flair to a team that had struggled to open up Palace in the opening hour.
Having missed the previous three league and cup games with a back injury, the Belgian substitute did not need long to make an impact after replacing Willian in the 64th minute with the score locked at 1-1.
Ninety-one seconds after his introduction, Chelsea were back in the lead after Palace’s defence failed to deal with Hazard’s free-kick into box allowing Morata to drill home.
Five minutes later it was 3-1, Pedro – who had delivered the pass for Morata to break the deadlock in the first half – with an unstoppable finish after Marcos Alonso’s low cross.
“We were in a little bit of trouble so we needed some quality, some personality,” added Sarri. “We were lucky today because Eden was on the bench so he was able immediately to change the match.”
Since arriving in the summer of 2017, Morata has struggled to convince his critics he is a consistent goal source for Chelsea.
Yet his performance against Palace could well win him a few more admirers even though he missed a chance to complete his hat-trick in the closing stages after being sent clean through by Hazard.
Will Palace stay out of danger?
Andros Townsend’s lovely equaliser after James McArthur sent him clean through raised hopes Palace could leave Stamford Bridge with a vital point.
Instead they are without a win in six league matches and must plan for their next game at home to Tottenham on the back of a fourth defeat in five top-flight games.
After Spurs next Saturday, Palace’s first game after the international break is at Manchester United on 24 November.
Having been knocked out of the Carabao Cup by Championship Middlesbrough in midweek, Palace started well against Chelsea.
With Wilfried Zaha causing problems at one end of the pitch and Mamadou Sakho strong at the other, Chelsea became frustrated until Morata scored with their first shot on target.
Chelsea have managed just two clean sheets in nine league and cup home games this season and Townsend’s quality finish against the run of play – only Palace’s eighth top-flight goal of the campaign – left them in sight of a first away point since 15 September.
Instead, Palace have now lost four in a row away from home and problems appear to be mounting for manager Roy Hodgson.
“The season has got a lot of football left in it and there’s many more games to play,” said Hodgson.
“I’m fairly confident with the players we have and the way we play that results will come. If you continue to perform at the right level the results have got to follow.”
Man of the match – Alvaro Morata
Good omen? – the stats
Chelsea are undefeated in their opening 11 Premier League matches of this season – they won the league in the previous two seasons they achieved this (2005-06 and 2014-15).
Blues boss Maurizio Sarri is unbeaten in his first 11 Premier League games as Chelsea manager – this is the joint-longest unbeaten start by a manager new to the Premier League, equalling the record set by Frank Clark in 1994.
Crystal Palace have taken just five points from their last 10 Premier League matches.
Chelsea’s Eden Hazard has assisted in three consecutive Premier League appearances as a substitute.
Chelsea’s Pedro has ended on the winning side in 39 of the 40 top-flight home matches he has scored in during his career (26 of 27 with Barcelona, 13 of 13 with Chelsea), drawing the other with Villarreal in January 2010.
Chelsea are on their Europa League travels to Belarus to face Bate Borisov on Thursday (17:55 GMT) while Palace face another tough match at home to Tottenham in the league next Saturday (17:30 GMT).