The 2-1defeat by Palace was West Ham’s fifth in six league and cup games this season.
Potter replaced Julen Lopetegui, who was sacked in January after six months in charge when West Ham were 14th in the table.
But former Chelsea and Brighton boss Potter found wins difficult to come by.
West Ham, who sold Ghana forward Mohammed Kudus to Tottenham for £55m in July, spent £126m on eight signings in the summer, including the £38m purchase of Portuguese midfielder Mateus Fernandes from Southampton.
But losses to Sunderland, Chelsea, Tottenham and Palace left them in the bottom three. They went out of the Carabao Cup in the second round with a 3-2 defeat by fellow strugglers Wolves.
That led to West Ham issuing a statement acknowledging “results and performances on the pitch over the past two seasons have not met the standards we set for ourselves”.
Disgruntled fans staged a demonstration against the board before the Palace match.
Poor results led to Potter becoming a viral trend on social media, with people using AI technology to swap his face on to other celebrities, including Barbie, US President Donald Trump and the Chuckle Brothers.
Speaking on Friday, Potter said he had not been taking it too seriously.
“It made my 15-year-old son laugh a lot, so you have to accept what comes with it,” he said.
“At times [that is] ridicule, but that is just the environment we are in and it is what it is.”
West Ham’s fortunes have declined since David Moyes’ departure a year after he won the club’s first trophy in 43 years in the Europa Conference League in 2023.
Potter’s arrival was supposed to herald a new brand of attractive football but the downward spiral has continued into this campaign.