Richarlison headed the crisis hit Merseysiders ahead early on but Blues fans were not happy with their team's defending.
Kalidou Koulibaly has been linked with Manchester United for some time but Blues fans want him at Stamford Bridge.
Chelsea's official Twitter account posted to inform fans Everton had taken the lead, and supporters wasted no time in the comments telling them where to splash their cash.
Thiago posted: "Buy Koulibaly and Chilwell first minute of the window."
And CFC Daily added: "Spend a billion on defence."
ForeverBlue tweeted: "Spend the entire budget on our defence," while Daniel Evans simply said: "First cross in the box and we concede. Unbelievable."
