The Everton players and manager were berated and subjected to jeers and whistles as they went over towards the travelling support after the final whistle.
Qatar-bound Jordan Pickford was partially at fault for the Cherries opener when the England goalkeeper spilled a Dominic Solanke shot into the path of Marcus Tavernier, who slotted home.
Kieffer Moore added a second in the 25th minute, before all three points were wrapped up by substitute Jadon Anthony in the second half.
"The performance was nowhere near good enough. It was nothing that represents Everton Football Club or our supporters."
— Everton (@Everton) November 12, 2022
Lampard believes the performance of his players warranted the reaction from the travelling fans. The Toffees were beaten 4-1 at the same venue in the Carabao Cup on Tuesday.
The Everton boss said: “The fans have a right to be disappointed because they’ve come down here twice this week and seen poor performances and before that we’ve been going OK. And then they see that there are performances that they don’t like.
“So when they see after Palace – and we can see that they gave us a welcome – they have to voice their opinion. And their opinions were right today.
They have to voice their opinion. And their opinions were right today
Frank Lampard on the Everton fans
“The players have to respect that the fans have a right to voice their opinions – and again they were right today.”
It was another long trip for the travelling support, who have now seen their team net just 11 goals in 15 Premier League matches.
The Toffees will finish the weekend just one point clear of the drop zone with manager Lampard severely under pressure going into the World Cup break.
Despite the reaction the players received from the travelling support, Lampard believes it was important for the players to go over to them.
He explained: “What was important today was the players went over to the fans, because they travelled down, they have to all go over.
“The players – albeit the performance wasn’t good enough – are not bad lads and they were disappointed. There’s things we need to speak about and the footballing level (was not good enough).”
Bournemouth ended a run of four successive league defeats with the win over the Toffees, but despite the recent wins over Everton, manager Gary O’Neil did not comment on his future at the club.
Incoming owner Bill Foley is finalising his purchase of Bournemouth and O’Neil has been interim manager since the Cherries’ 9-0 thrashing at Liverpool in August.
O’Neil explained: “I don’t want to comment on things that haven’t been confirmed yet by the club.
“I’ve been in constant dialogue with them but I don’t think it would be fair of me to comment on things that haven’t been confirmed yet.”
Marcelo Bielsa is one of the names that has been linked to the vacancy at the Vitality Stadium, and the current Bournemouth interim head coach believes he would do well at the club.
O’Neil added: “(I have) huge respect (for Bielsa). There’s been noise for the last couple of days so huge respect for Bielsa and what he’s achieved and his reputation and the work he’s done is fantastic.
“So I’m sure if Marcelo Bielsa was to come to Bournemouth then he would do a good job.”