The party has been engulfed by infighting after the claims made in last week’s BBC Panorama, with two whistleblowers who featured in the programme now threatening to sue as a result of the the Labour reponse.
Ms Thornberry said the party should be addressing the issues, rather than attacking ex-staff who spoke out about what was happening in the party.
Labour continues to complain about the documentary, which claimed that senior figures – including party leader Jeremy Corbyn’s communications chief Seumas Milne and the party’s general secretary Jennie Formby – had interfered in antisemitism investigations.
Mr Corbyn said the documentary had contained “many, many inaccuracies”, as he addressed the Durham Miners’ Gala on Saturday.
However, Ms Thornberry said the party needs to face up to the fact that it still has a problem with antisemitism.
“I think that we shouldn’t be going for the messengers, we should be looking at the message. I think that is what is important,” she told the BBC’s Andrew Marr show yesterday.
“Nobody can pretend that there isn’t an ongoing problem within the Labour Party about antisemitism, about our processes for dealing with it.”
However, shadow chancellor John McDonnell insisted the problem was being dealt with, with new systems having been put in place.
“There’s always lessons to be learnt, but I think the way Jennie Formby, our general secretary, has operated, implemented the measures, is getting on top of this,” he told BBC Radio 4’s World At One.
Ms Thornberry also criticised deputy leader Tom Watson for attacking Ms Formby while she was undergoing treatment for cancer.
“I wish he wasn’t attacking somebody who is going through chemotherapy. I think that is a mistake,” she said.
“She is the general secretary of the Labour Party but we know that she is very ill. I think it is completely inappropriate to personalise this.”
Her comments followed a bitter tirade from Unite union general secretary Len McCluskey, who said Mr Watson “and his pals” should “f****** well be ashamed of yourselves”.
To cheers from the crowd at Durham Racecourse, he declared: “Jennie, our message to you is that the Durham Miners’ Gala stands with you.”