The retired Anglican was warned earlier in the week to expect "explicit criticism" over his support for Peter Ball, former Bishop of Gloucester and Bishop of Lewes.
Ball, 84, was jailed in October 2015 for abusing 18 young men between 1977 and 1992.
A source close to Carey told The Sunday Telegraph: "He knows he will be criticised and he knows he will be criticised rightly.
"Clearly the Church didn't handle it well and Lord Carey was naive in trusting peter ball.
"The acknowledgment now is he wasn't doing the Christian thing by the victims of Ball. He would accept he didn't discharge the pastoral duties to the victims very well."
He has now been given his own lawyer to represent him in a national child abuse inquiry, investigating abuse in England and Wales, including in the Church.
He had previously been using the Church's lawyers, however request his own last month over concerns of 'conflict' between himself and the Church.