Bishop George Bell, who died 60 years ago, was accused of abusing a girl in the 1950s but a review this week found that the inquiry was deficient and that the Church of England 'rushed to judgement'.
Those who believe the Bishop to be innocent say his reputation has been destroyed.
But the Archbishop of Canterbury only appeared to criticise the fact that the church named Bell, saying: "'The decision to publish his name was taken with immense reluctance, and all involved recognised the deep tragedy involved."
He added in the statement: "No human being is entirely good or bad. Bishop Bell was in many ways a hero. He is also accused of great wickedness. Good acts do not diminish evil ones, nor do evil ones make it right to forget the good. Whatever is thought about the accusations, the whole person and whole life should be kept in mind."
Lord Carlisle, who conducted the review, said Archbishop Justin's comments were: "less than fully adroit."
According to the Daily Mail, Dr Ruth Hildebrandt Grayson, the daughter of Bishop Bell's friend Franz Hildebrandt, said the bishop's family deserved a personal apology from the Archbishop and the Bishop of Chichester.
'The Church can't have its cake and eat it,' she said. 'Either he is innocent, in which case they must apologise, or he is guilty, which they can't prove, and the report makes clear that they have not proved.'
Professor Andrew Chandler, Bell's biographer, said the Archbishop's statement was 'wrong' and 'illogical'.
Rev Gavin Ashenden wrote in The Times that the Church needs to be committed to the truth.
The trashing of the posthumous reputation of a man revered for integrity and courage has caused widespread alarm and concern.
— Gavin Ashenden (@gavinashenden) December 16, 2017
"In this, as with other matters, the C of E, needs to be more committed to the value of truth than it is to seeking pubic approbation."@Justice4Bell pic.twitter.com/o16RfN75lf
