The next Archbishop of Canterbury Justin Welby has referred to the Church of England's women Bishop vote during an exchange with George Osborne during a session of the independent Banking Commission - and received a sympathetic response from the Chancellor.
He said the Anglican Church has its own processes which should be respected, but added that it needs a "sharp prod".
The Archbishop of Canterbury Dr Rowan Williams has said the Church of England has "undoubtedly" lost a "measure of credibility" in wider society following the defeat of the legislation to introduce women Bishops to the church.
He told the General Synod: "Whatever the motivation for voting yesterday whatever the theological principle on which people acted and spoke, the fact remains that a great deal of this discussion is not intelligible to our wider society.
"Worse than that, it seems as if we are wilfully blind to some of the trends and priorities of that wider society.
"We have some explaining to do, we have as a result of yesterday undoubtedly lost a measure of credibility in our society."
The Archbishop of Canterbury, Dr Rowan Williams, said the Church of England has a "lot of explaining" to do after rejecting legislation introducing the first women bishops.
The Archbishop of York's press officer Kerron Cross has tweeted the outgoing Archbishop of Canterbury Rowan Williams has told the Synod the church's vote to reject women bishops has lost the Church of England credibility.
Speaking on BBC Radio 4 this morning, the Archbishop of York, John Sentamu, has said the vote was "very disappointing" but he remained hopeful for the future.
The Archbishop of Canterbury will make a statement today after the Church of England rejected legislation that would have paved the way for women bishops.
Dr Rowan Williams is due to speak as the Church's national assembly gathers after the legislation failed to gain the necessary two thirds majority amongst lay members.
His statement will come after an emergency meeting of the Church of England bishops following the narrow defeat.
Labour MP for Durham City Roberta Blackman Woods, Conservative MP for Torridge and West Devon Geoffrey Cox and Liberal Democrat MP for St Austell and Newquay Stephen Gilbert have tweeted:
V disappointed by Church of Eng vote on women bishops Hope Justin Welby can make progress & correct this wrong unrepresentative vote #Synod
Synod decision is the democratic and legitimate expression of the government of the church and should be respected even if we disagree.
"One speaker said, as if it mattered: "I don't believe that this is legislation that will allow the world to look at the church tonight and see Jesus Christ"; and no one pointed out that back on planet earth, the world will look at the church today and say: 'Jesus Christ!'"
"The decision is remarkable but understandable given the Anglican Church's paralysis. On the one hand, it has become the Labour Party at prayer – fixated on equality. On the other, its obsession with showing respect to conservatives means that it cannot commit to its own egalitarian principles."
"Yesterday was a sad and shameful day for the Church of England and therefore for the country of which it is the established religion. It took 12 years of deliberation and prayer for the Church to arrive at its decision on appointing women as bishops, and yet it got that decision dreadfully wrong."
The Revd Canon Dr Giles Fraser, former Canon Chancellor of St Paul's Cathedral, said of today's result:
The Church of England has become a national disgrace.