The MP for Birkenhead announced he would sit as an independent on Thursday after 40 years representing Labour in the Wirral seat.
Field said he has been subjected to online abuse since his decision, with one user calling him a "Tory rent boy" who should "f*** off and die".
An email sent to him read: "The claim of antisemitism is obviously bogus AND YOU KNOW IT. Israel is the purest [evil] on earth and you are siding with them."
Field told The Mail on Sunday: "Sadly, this provides a snapshot of the bile that exists beneath public life."
Meanwhile, the Labour leader has said Field did not have to resign the Labour whip over the anti-Semitism row.
While Jeremy Corbyn said he was "sorry" Field had resigned, and condemned bullying, he insisted that there had to be "democratic debate within the party".
Asked about Mr Field's claims of bullying in the party, Corbyn said he did not know what the claims were.
"I invite all MPs to take part in the discussion and the debate," he said.
"Obviously bullying and intimidation have no place whatsoever in any political party, particularly the Labour Party, but there has to be democratic debate within the party."
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