Asked by Ms Barnett whether she felt this was acceptable, Ms Berger said: "I will judge Keir Starmer on his actions now in the wake of the report."
She added: "Ultimately the responsibility rests with Jeremy Corbyn who was leader at the time.
"There were people in all areas of leadership who could have done more."
Ms Berger also revealed that Angela Rayner, Labour's Deputy Leader, had called her on the eve of the EHRC report's publication.
Since quit Labour in February 2019 after citing allegations of bullying and antisemitism in the party.
Ms Berger had taken a lead role in highlighting Labour's problem with anti-Jewish racism under Mr Corbyn.
She had challenged him openly over his remarks on the antisemitic mural in Tower Hamlets