Figures from the Corporation's annual report show that ethnic minority, LGBT, disabled and female senior bosses get paid more than people who are not from these categories.
Samir Shah said that the Corporation had not done enough to show it was in touch with the concerns of working people, including on migration, pressures on housing and public services.
The journalist, 45, who currently presents the BBC's News at One and was the Corporation's Beirut-based Middle East correspondent, will replace Ms Husain, who left the BBC last year.
The Corporation is offering the salary for a Head of Diversity, Inclusion and Belonging who will be in charge of creating 'an inclusive workplace culture where everyone feels they can belong'.
Samir Shah said the row, which blew up after it emerged that the programme had been narrated by the 13-year-old son of a Hamas official, was a 'really bad moment' for the BBC.
If such behaviour had been exposed, it would have been a catastrophe for the BBC, would likely have led to prosecutions and might even have caused the collapse of the Corporation.