Police and match stewards intervened during heated exchanges involving the travelling support and club captain Seamus Coleman, with manager Frank Lampard seen pulling Jordan Pickford away after the full-time whistle.
Alex Iwobi was also among the players to approach the away end, throwing his shirt into the crowd only to see it thrown straight back moments later.
The defeat to Bournemouth is Everton’s second at the Vitality Stadium in the space of four days, having lost 4-1 to the Cherries in a Carabao Cup tie midweek. The latest setback for the Toffees leaves them sat in 17th place heading into the World Cup break.
Lampard appeared to apologise to fans during the chaotic scenes at full-time, attempting to defuse the situation.
‘I can’t talk you through it but the fans have their dues to be unhappy today,’ Lampard told Sky Sports.
‘They travelled down to support the club and they are brilliant for us and today they can show what they feel about the game. They probably feel like I do.
‘Everton defender Conor Coady admitted post-match Bournemouth simply ‘wanted it more’ with Lampard agreeing with his sentiment.
‘You can’t win football matches like that. They were sharper than us, more aggressive than us and that is the responsibility of the players, and mine.
‘I can’t run on the pitch but I can talk to them before the game, at half-time, but they have to show the reaction on the pitch and they didn’t show that today.
An error from Pickford in the Everton goal saw Bournemouth take an early lead with Marcus Tavenier pouncing after the England goalkeeper failed to hold onto Dominic Solanke’s shot.
Kieffer Moore doubled his sides lead with a header seven minutes later with Jaidon Anthony wrapping up the win with a header of his own after 69 minutes.
Everton head into the break on a run of one win in seven league games, sat just a point above the relegation zone and four from bottom.
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