Around 100 Everton fans stayed behind for 90 minutes to protest against manager Roberto Martinez following Saturday's 2-1 win over Bournemouth.
Supporters displayed banners that read "Martinez out" and called for chairman Bill Kenwright to step down.
Another banner that read "Time to go Roberto" was flown over Goodison Park during the match.
"Those aspects [the protests] are not for me. My concentration is on preparing for the game," said Martinez.
The protesters who had stayed in the ground eventually dispersed around 18:15 BST.
The win was only Everton's fifth at home in the Premier League this season, and their first win in eight games in all competitions.
"Football is a game full of passion and emotions and I understand what comes when you have not won enough games," Martinez added.
"I can understand we have been through a very painful time but we had high hopes; we wanted to get into the FA Cup final and we have had eight league defeats at home.
"I cannot hide that it is a real disappointment for all of us, not just me. We want to learn from the mistakes.
"My intention is to win football games and to be successful and that doesn't change."
'Fans were determined to have their voices heard'
Martin Fisher, Match of the Day's commentator at Goodison Park on Saturday, witnessed the protests after the match.
"During the game I didn't see any anti-Martinez banners, nor did I hear any negative chants aimed at the manager by the fans. There were muted boos on the half-time whistle and a few grumbles during play but overall I was struck by the silence around the ground and that in itself probably spoke volumes.
"It was only after the final whistle that banners were revealed. There were probably about a dozen. Some were on bedsheets, others on printed cards.
"It was a peaceful demonstration but interestingly the PA system blared out loud music for about an hour to drown out any chants. The fans stayed - determined to have their voices heard - and when I left Goodison I could hear the chant 'You're getting sacked in the morning' being sung with some gusto."