LONDON — In a sign of deepening crisis in the Church of England after it rejected the appointment of women as bishops, its spiritual leader said Wednesday that the church had “undoubtedly lost a measure of credibility” and had a “lot of explaining to do” to people who found its deliberations opaque.

The archbishop of Canterbury, the Most Rev. Rowan Williams, was speaking after an emergency meeting of bishops called to debate Tuesday’s narrow balloting by its General Synod rejecting the ordination of women as bishops, even though female priests account for one-third of the Church of England’s clergy members.

Female priests hold senior positions like canon and archdeacon, and some had been hoping to secure appointments as bishops by 2014 if the change had been approved.

The vote represented a direct rebuff to Archbishop Williams’s reformist efforts during his 10 years as head of the church and a huge setback to a campaign for change that has been debated intensely and often bitterly for the past decade.