A BBC investigation found Cottrell renewed David Tudor's contract as area dean in Essex on two occasions as bishop of Chelmsford.
Tudor had previously been barred from ministry for five years for having sex with a 16-year-old girl who was a pupil at a school where he was chaplain. He paid her compensation, and he was banned from being alone with children.
Cottrell admitted that things "could have been handled differently".
The scandal is the second high-profile crisis to envelop the Church of England in recent months.
The church's leader, the archbishop of Canterbury, Justin Welby, announced his resignation in November in the wake of the Makin report, which found Welby could have brought the serial abuser John Smyth to justice if he had reported him to police in 2013.
Cottrell will become the church's most senior figure when Welby steps down next month.
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