The Bishop of Chichester and the Bishop of Lewes have issued a joint statement to apologise for abuse in the 1970s and 80s by a paedophile priest.
They said they apologised "unreservedly for any past mistakes which may have left children vulnerable".
A review found significant failings in the church which ordained Roy Cotton, despite him being convicted of child abuse.
The bishops said they were "determined to learn form the experience".
The joint statement from Bishop of Chichester, the Right Reverend John Hind, and Bishop of Lewes, Right Reverend Wallace Benn, reads: "We wish to put on record our profound sadness and regret for the pain caused to all who have been abused in the Diocese of Chichester.
"The abuse of children under any circumstances is a tragedy and an affront to their human dignity.
"This is a particular betrayal when it is committed in the church where people should be safe and respected.
"The abuse committed by the priests... is particularly harrowing and we are determined to learn from this experience and do all that we can to create and maintain the safest possible environment for all involved in the life of the Church.
"We apologise unreservedly for any past mistakes which may have left children vulnerable and which may have more recently made victims feel that they have not been taken seriously.
"We are also both very sorry for any weaknesses in implementation of our procedures that may have compounded the problem for victims.
"Recent changes in policy and practice have already been introduced. Although we are confident in our current policies and procedures, we shall subject them to continuous independent scrutiny."
The church-commissioned report by Baroness Butler-Sloss, which was released in May, criticised both senior clergy and Sussex Police over how they dealt with historical claims of abuse by Cotton and Colin Pritchard.
In the report, she said across the diocese "and probably in many other dioceses" there had been "a lack of understanding of the seriousness of historic child abuse".
The retired senior judge said the victims' claims were not taken seriously and she believed Cotton had at least 10 victims.
Pritchard served as the vicar of St Barnabas, Bexhill, until 2007 after being arrested over sex abuse claims. In 2008 he pleaded guilty to sexually abusing two boys and was jailed for five years.
The offences took place while he was parish priest at St Andrew's Church in Wellingborough, Northamptonshire.
The court heard that Cotton had been involved in the offences but died in 2006, two weeks before Pritchard was arrested. Cotton worked as a priest in Brede, near Rye, in the 1990s.