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.
Dr Williams said the Church of England had "undoubtedly" lost a "measure of credibility" in wider society following the defeat of the legislation.
"We have, to put it very bluntly, a lot of explaining to do," 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 vote on Tuesday evening came in spite of 42 out of 44 dioceses in the Church of England backing the legislation.
Dr Williams said the Church of England "rightly" insisted on a high level of consent for change.
"Failure to secure a two-thirds majority in the House of Laity does not mean that those high levels of consent are necessarily wrong; they do mean that there is a great deal of further work to do done," he said.
"But that sense of Synod which, for admirable, praiseworthy reasons, gives very strong voice to minority, that sense of Synod needs some explaining and some exploring if it is not simply to be seen as a holding to hostage of Synod by certain groups. That's part of the explaining we need to do."
Downing Street said prime minister David Cameron shared the disappointment at the result but stressed that it was a decision for the Church rather than government or Parliament.
His spokesman said: "His personal view is that there should be women bishops and he shares the disappointment of the Archbishop that the Synod was unable to take this forward.
"But it's for the Church to make a decision on."