Everton director of football Marcel Brands held face-to-face talks with angry fans at the club's training ground on Monday following their FA Cup defeat to Liverpool.
A small group of supporters arrived at Finch Farm on Monday morning to confront the squad after their 1-0 defeat to an inexperienced Liverpool side the previous evening.
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The fans intended to meet the squad and question their commitment to the club but were unable speak to the players, who were away on a day off.
Brands, however, met with the supporters and listened to their complaints.
It comes after midfielder Fabian Delph was allegedly involved in a heated exchange with a fan on Instagram after the defeat at Anfield.
Sky Sports News understands Everton have launched an investigation into the matter.
The protests at Finch Farm have come just weeks after Carlo Ancelotti's appointment as the club's new manager.
The Toffees are currently 11th in the Premier League and next face Brighton at Goodison Park on January 11.