Addressing the Jewish Labour Movement one-day conference on Sunday morning, Ms Rayner said: “Our members need to get real about this.
“If they don’t think anti-Semitism is within the Labour Party and that there are problems now, then there’s really no place for them in the Labour Party.”
“If they think making people feel unsafe or unwelcome in our meetings is a response to the EHRC (Equality and Human Rights Commission) report, then they need to be out of our party immediately.
“People need to understand what our Jewish community have been through.”
The report released in October pointed to “unlawful acts of harassment and discrimination for which the Labour Party is responsible”.
The deputy leader added: “We should have a bit of humility… We should be listening and aware of how hurt and upset people are.”
She continued: “If I have to suspend thousands and thousands of members, we will do that.
“Because we cannot and we will not accept an injury to one, because an injury to one is an injury to all. That’s what we say in our movement.
The deputy leader said it was also a matter of “education”, adding that while it was generally right for a party to debate issues, “there’s no debating what the EHRC said”.
“There’s no debating whether anti-Semitism exists in the Labour Party. It does, and we’ve got to do everything we can to stamp it out.”
He was later reinstated as a Labour member by the National Executive Committee following a meeting of a disciplinary panel three weeks later.
Turning to Mr Corbyn’s comments, Ms Rayner said: “What Jeremy said in response to the EHRC report was totally unacceptable.
“Any attempts to minimise or downplay the extent of anti-Semitism are part of the problem. This is the issue.
“I knew this would happen. It is a matter of public record now that I contacted Jeremy to try and get him not to say what he said, and to apologise and withdraw it afterwards.
“Because I don’t think Jeremy really quite gets how upsetting it is."
She continued: “I just want to say that I really do hope that Jeremy really does reflect now on what he said on the day that report was published and his response to that.
“I truly hope he reflects. I understand that he thinks he’s always tackled issues of anti-Semitism.
“I understand he thinks he’s always tackled issues of racism. But on this, he’s wrong. He has to accept as a leader that we failed.
“We all have to accept that. I’ve accepted my failure in that. Then we’ve got to go and make sure that we do everything we possibly can to regain that trust and respect.
“I don’t think Jeremy has done enough for that now, no, so at the very least I think he should apologise, absolutely.”