Oliver Glasner’s side now sits 15th in the Premier League table with a difficult schedule ahead.
Speaking after the match, McFarlane maintained the win was crucial to break the cycle of negative results under Rosenior.
Man City will face the winner of the Chelsea-Leeds United semifinal next month.
Erling Haaland scored the only goal of the game.
The Blues’ poor run also included defeats to Paris Saint-Germain in the Champions League.
Harry Maguire and Lisandro Martinez both missed the game due to suspension.
Doku expressed optimism that City could still win the title despite the six points gap between them and Arsenal.
Chelsea manager Liam Rosenior said the player “crossed a line” in the club’s culture.
Beto doubled the lead for Everton for the hosts in the 62nd minute, firing home a shot from close range that slipped in between Sanchez’s legs.
Chelsea have also been banned from registering new academy players for nine months, with the punishment taking effect immediately.
