However, while Sarri has stopped short of saying anything about the next line of action for Moses, the gaffer spoke at length about one of the winger's rivals, Ruben Loftus-Cheek. Will have easier days in this league but if you're sloppy in possession like Milivojevic was today then it doesn't help.
Moses established himself as a key figure at right wing-back under Antonio Conte, but Sarri's arrival has seen Chelsea switch to a 4-3-3 formation and the Nigerian is once again battling for minutes on the wing with Eden Hazard, Pedro and Willian.
The two forgotten members of the Chelsea squad are Victor Moses and Danny Drinkwater, two players with Premier League title to their name in recent years.
"I think also Alvaro has a very great potential, physical potential, technical potential, so he has to improve more". He said: "I don't know. They have to improve but their characteristics are a little bit different".
It's an interesting topic, particularly with the midfield options Sarri does have at his disposal and the fact that Kante has played every minute of Premier League football so far this season.
"He came off after about 67 minutes and at that point I wondered "well, maybe he's saving him for Sunday".
"I think that here I have been lucky".
Eden Hazard was named on the substitute's bench, having missed Chelsea's last three matches through injury and he was clearly missed as Palace impressed in the opening exchanges.
Meanwhile, Crystal Palace are enduring a tough second season under Roy Hodgson and are now 14th in the Premier League, winless in their last five.
'I can score hat-trick [so it] is not ideal day but we take three points, we are in first three places. "I told him two months ago what I think", Sarri told reporters before talking about Moses. We need to cover immediately the lost ball. When I arrived here the gap was 30 points, so the first step is to try and cover the gap.
"I didn't ask anything about it to my club at the moment because I think we can stay with these players and be competitive".
"For now, I have to send to my players the message that only this match is important". It is not easy to play for Manchester City, Manchester United, Juventus. More often than not he is double-marked, with any opposition team safe in the knowledge they do not have much else to worry about.