The vote in the House of Laity fell short of approval by six votes.
Lay members of the deanery synods elect the members of the general synod's House of Laity.
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The measure was passed by the synod's houses of bishops and clergy but was rejected by the House of Laity.
He said this was reflected in the opinion of House of Laity.
The vote in the House of Laity, at 64%, was just short of the required majority - six more "yes" votes were needed.
The House of laity is the largest element of the General Synod and is made up of lay members of the church elected by its 44 dioceses.
BBC: Women bishops: Church of England general synod votes against - BBC News
The proposed legislation paving the way for the change fell short by six votes in the House of Laity - one of the synod's three houses.
The proposed legislation for ordination of women bishops was passed by the synod's houses of bishops and clergy but was rejected by the House of Laity last month.
He rejected accusations by supporters of women bishops that a well-organised campaign had skewed representation in the House of Laity, which he insisted reflected opinion in the church as a whole.
The measure to allow women to be bishops passed in the synod's Houses of Bishops and Clergy on 20 November, but failed to gain the required two-thirds majority in the House of Laity.
The votes were 44 for and three against with two abstentions in the House of Bishops, 148 for and 45 against in the House of Clergy, and 132 for and 74 against in the House of Laity.
The proposed legislation paving the way for women bishops needed to gain two-thirds majority support in each of the synod's three houses - bishops, clergy and laity - but fell short by six votes in the House of Laity.
BBC: Church of England's decision on women bishops was 'wrong'
"It is impossible for me to explain to parliamentary colleagues how a measure that has had the support of 42 out of the 44 dioceses failed to pass in general synod, " Sir Tony said, questioning whether the election process to the House of Laity was "sufficiently representative".
He blamed a "handful of votes amongst the laity" for the failure to secure the requisite two-thirds majority in each house of the tricameral legislative body.
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