He made the remark during a meeting of the Palestinian Return Centre when talking about an earlier speech from Manuel Hassassian, the Palestinian envoy to the UK.
Mr Corbyn is heard describing Mr Hassassian's speech as “incredibly powerful, passionate and effective about the history of Palestine and the rights of the Palestinian people.”
He continues: “This was dutifully recorded by the thankfully silent Zionists who were in the audience on that occasion, and then came up and berated him afterwards for what he had said.
“They clearly have two problems. One is that they don’t want to study history, and secondly, having lived in this country for a very long time, probably all their lives, don’t understand English irony.”
Ms Berger tweeted: "The video released today of the leader of @UKLabour making inexcusable comments - defended by a party spokesman - makes me as a proud British Jew feel unwelcome in my own party.
"I've lived in Britain all my life and I don't need any lessons in history/irony."
A spokesperson for Mr Corbyn denied the comments were offensive: "He was referring to a group of pro-Israel activists misunderstanding - and then criticising - the Palestinian ambassador for a speech at a separate event about the occupation of the West Bank."
On the Today programme, shadow chancellor John McDonnell defended Mr Corbyn’s comments.
He said: “I think this has all been taken out of context, whatever Jeremy has said throughout the years has all been about how to secure peace particularly in the Middle East. But also peace with Justice for all concerned, both members of the Jewish community and the Palestinian community, in that context Jeremy has devoted his life.
“To take comments like that out of context is not helping. In certain contexts certain phrases are appropriate and to take them out of context is unacceptable.”
He suggested drawing attention to Mr Corbyn’s comments was “exacerbating the issue.”
“Where we want to get to now is let’s recognise there is antisemitism in our society let’s have a real serious debate about the actions needed to tackle that antisemitism where ever it is displayed.”
Mr Cobyn’s comments were endorsed by the former leader of the far-right British National Party.
Nick Griffin, the self-declared “lifelong white rights fighter,” shared his support for Mr Corbyn on Twitter.
He wrote: “Go Jezza! I wonder how many Labour activists the hysterical #Zionist media campaign against #Corbyn is re-pilling?”
