The Anglican leader was accused by Andrew Morse of being "staggeringly hypocritical" after he suggested the Corporation was not as willing as the Church of England to admit to its mistakes over the scandal.
Mr Morse is among the alleged victims of John Smyth (pictured below) - who, it's claimed, carried out savage beatings against boys at the Iwerne summer camps. Archbishop Justin was a dormitory supervisor at the camps during the 1970s.
Mr Morse told the Mail on Sunday: "It is just staggering hypocrisy to criticise an institution for inappropriate coverage of abuse when almost unanimously victims who have had to deal with the Church have really been treated absolutely appallingly.
"Having heard what he said today, I think he should resign."
Speaking on BBC Radio 4 on Saturday, Archbishop Justin said: "I haven't seen the same integrity over the BBC's failures over Savile as I've seen in the Roman Catholic Church, in the Church of England, in other public institutions over abuse.
"We may be proved wrong about that..."
A BBC spokesman said it didn't recognise the "characterisation" made by Archbishop Justin. They pointed out that the corporation published the full details of an independent investigation following the scandal.
Speaking with BBC News, they added: "We set out very clear actions to ensure the highest possible standards of child safeguarding."
A spokeswoman for Lambeth Palace said the Church of England fully accepts its own failures in the area of safeguarding, adding that Archbishop Justin's been clear protecting the young and vulnerable should be the church's "highest priority".
Highlighting the creation of the Church's National Safeguarding Team in 2015 and new policies, she added: "The Archbishop believes this level of rigorous response and self-examination needs to extend to all institutions, including the BBC."