He also appeared to suggest that here had been significant progress in the fight against antisemitism within Jeremy Corbyn's party since Mr Caplin took over as JLM chair just weeks ago.
Listen to the interview below
He told the LBC presenter: "Is there a problem with antisemitism in the Labour Party? Yes there is.
"Are we trying to deal with it? Yes we are. Nick, you have to make small steps to make bigger steps.
"I picked up this battle just two or three weeks ago as chair of the Jewish Labour Movement.
"There have been extensive discussions about how we deal with antisemitism and get it right.
"And I am already starting to see the small steps that I wanted to see in month one."
Having heard the LBC interview with Mr Caplin, one senior JLM official told the JC: "I couldn't believe what I was hearing. It actually made me feel sick."
Mr Caplin did his radio interview on Tuesday, a day after he attended a meeting with Labour Party General Secretary Jennie Formby where he was shown the party's controversial new guidelines on antisemitism.
But during his LBC appearance, Mr Caplin seemed to be pleased with the message he had been given by Ms Formby.
He told Mr Ferrari: "I think we are starting to see the progress I wanted to see."
Speaking at the (HET) conference on Monday, Dr Lipstadt said antisemitism has become “embedded” in Labour and it has become more socially acceptable to "make a crack" at a dinner party about Jews.
Dr Lipstadt, who won a legal battle against historian David Irving in 2000 after he sued for libel when she labelled him a Holocaust denier, said her victory had weakened what she described as “hardcore" Holocaust denial but said we were now witnessing a “softcore” form of the same.
Arguing that the Labour Party had played a part in the rise of this “softcore” form of denial, she said: “You have a former mayor here in London [Ken Livingstone] who would talk about the cooperation between the Zionists and the Nazis.
“He took one little historical fact and blew it up into something that never existed, completely twisted the truth. Irrespective of how you feel about him politically, it's historically rubbish."
She also suggested that Mr Corbyn is at best “blind to overt manifestations of antisemitism”, referring to his questioning of a London council’s decision to destroy an antisemitic mural which depicted a group of Jewish bankers counting money.
Mr Caplin, a former defence minister in Tony Blair’s government, was confirmed as JLM chair in June.
A former Labour MP for Hove, in Sussex until 2005, Mr Caplin replaced former chair Jeremy Newmark after he resigned earlier this year.
