The Brazil global netted a stunning goal to secure his side a 2-1 win over Stamford Bridge on Saturday evening.
Newcastle have now lost 10 in a row away to the division's established top six, but they put up a good fight in West London, levelling up through Ciaran Clark after Pedro opened the scoring, only for Willian to win the match for Chelsea.
The 40-year-old went on to say Newcastle fans should be grateful Ashley appointed Rafael Benitez as manager, also describing the north-east side as "a yo-yo club" and adding: "He wants to sell the club, why should he go and spend millions of pounds?" [If] the club is anxious, I don't know.
The former Napoli manager responded similarly to talk Willian potential exit in an interview with Sky Sports, claiming: "You know very well that Willian is a very important player".More news: GOP Sen. Lindsey Graham: Trump isn't giving in on southern border wall
"As you have seen, today Jorginho was in trouble and on the bench there wasn't a player for that position, so I need a player, I need an option for Jorginho", the Italian explained.
On his decisive goal and the win over Newcastle, he added: 'I think it's always hard in the Premier League.
"In my opinion Willian has to stay with us".
Willian was unable to double his tally when, like Pedro before him, he was played through with a simple lofted pass, with Dubravka this time getting a touch to the attempted lob. [Hudson-Odoi] is becoming for us a really important player.More news: House GOP leader vows action against King over racist remarks
The Blues boss said: "After the goal I think we thought "now it's easy", but it wasn't".
Sources have told ESPN FC it would take a significant cash bid for Chelsea to consider parting with Willian, regarded by Sarri as a key first-team player. We stopped to play and then we had problems.
"We need to improve in the mental reaction". With Eden [Hazard] as a striker, we need wingers. We need Hudson-Odoi. We need Willian of course. I am very happy here.
But it took only nine minutes for the Blues to go in front as Newcastle's five-man defence was carved open easily.More news: Israel claims Syria air strike, says hunt for Hezbollah tunnels over