The Prime Minister David Cameron has told the Commons, the time is right for women Bishops and the Church of England needs to "get with the programme".
ITV News' Social Affairs Editor Penny Marshall says the Synod was left "shell-shocked" by the decision to reject women Bishops and the damage caused by the vote has been immense.
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 Prime Minister's spokesman says David Cameron's personal view is that there should be women bishops and he shares the disappointment of the bishops over last night's defeat on the issue.
But the spokesman stresses that it is "clearly up to the church to decide". He says there are "no plans to change the rules" on the Equality Act, from which the Church of England is currently exempt.
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.
++Rowan "We have lost a level of credibility in the wider society based on yesterday." #synod
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.