Everton announced Marcel Brands had left his position as director of football on Sunday but said under-fire manager Rafa Benitez has their "full support".
Everton's 4-1 defeat by Liverpool on Wednesday stretched their winless run to eight games and left them 16th in the Premier League, five points above the relegation zone.
Brands was confronted by fans as he left the director's box after that defeat.
"The owner and directors would like to thank Marcel for the service he has given to the club over the past three and a half years and wish him well for his future," the club said in a statement
"In the meantime, the owner and board of directors will continue to provide our manager, Rafa Benitez, with their full support."
Everton added that a strategic review would be conducted to ascertain the club's long-term plans for the future.
(Reporting by Aadi Nair in Bengaluru; Editing by Peter Rutherford)