Maurizio Sarri was mystified by Chelsea's sudden drop-off at Everton and admitted a Premier League top-four finish would be "impossible" if they do not improve.
The Blues dominated possession and territory in the opening half at Goodison Park, and Eden Hazard saw a deflected strike come back off a post, but the visitors faded badly after the interval.
In contrast, Everton were rejuvenated and sealed a 2-0 win by virtue of Richarlison's header shortly after the resumption and Gylfi Sigurdsson scoring on the rebound after his 72nd-minute penalty was saved.