The outgoing Archbishop of Canterbury gave his final Christmas Day sermon on Tuesday, live-tweeted by the Anglican leader's office for the first time.
Rowan Williams, who steps down at the end of December after a decade as leader of the world's 80 million Anglicans, acknowledged in the sermon that the Church of England had damaged its reputation by rejecting women bishops.
Speaking at Canterbury Cathedral in Kent, southeast England, Williams said last month's failure by England's state church to approve the new measure had been "deeply painful".
The vote was a final setback for Williams, a liberal who has battled over the last decade to bridge bitter divides with the church's traditionalists.
He added that Christians must not lose heart after census statistics showed this month that Britain is apparently becoming a less faithful nation.
The proportion identifying themselves as Christian dropped from 72 percent in 2001 to 59 percent in 2011.
But Williams insisted: "It remains true that three quarters of the public still want to identify themselves as having a religious faith of some kind."
The sermon was live-tweeted by William's Lambeth Palace residence, and his successor Justin Welby -- who takes office in March -- also tweeted his own final Christmas sermon as Bishop of Durham.
Williams has never tweeted himself but Welby, a former oil executive, is a keen user of the social networking site and has said he has no plans to stop.
Like Williams, Welby supports the introduction of women bishops.
The Church of England is set to present its governing General Synod with revised plans on the bishops next July.
The wider Anglican communion's first woman bishop was appointed in the United States in 1989 and there are now 37 worldwide