He was replaced by young forward Hudson-Odoi, who has been nursing a hamstring problem of his own and was himself taken off towards the end of the game at Vicarage Road.
Sarri faced continued questioning from reporters about the decision to move him into the middle, but sees no issue with using Hazard's flexibility to play in both roles.
Links with a move to Real Madrid for the Belgium worldwide have persisted, with the winger recently refusing to be drawn on whether he would commit long term to Chelsea and extend a contract that expires at the end of next season.
However, the 26-year-old signed a contract extension in August with Palace until 2023, making him the club's best paid player in the process.
When asked whether the Belgian will be at Stamford Bridge next season, Sarri said: "I don't know but it's time to decide", according to FourFourTwo.
Sarri, however, warned that losing Fabregas during the season would complicate his job.
Hazard reiterated after scoring twice in Chelsea's 2-1 win over Watford on Wednesday that he intends to postpone any firm decision on his future until the end of the season - a stance meant to keep his options open if Real Madrid decide to make a push to sign him. Will I sit down with him?
Hudson-Odoi played a key role in England's 2017 Under-17 World Cup victory, appearing in all nine matches and setting up three goals in the 5-2 victory over Spain in the final. You have to manage 25/28 players.
Many pundits and bookmakers believe that Eden Hazard will be on his way out of Chelsea next summer and join Real Madrid.
Kovacic became a Chelsea player shortly after playing a part in his country's surprise run to the final of this summer's FIFA World Cup tournament in Russian Federation.