A draft paper issued at a Catholic Church synod in the Vatican had included text calling for greater openness towards homosexuals, and divorced Catholics who remarried.
But this failed to win two-thirds backing and was not in the final text.
The synod will reconvene next year.
The New Ways Ministry, a US Catholic gay-rights group, said it was "very disappointing that the synod's final report did not retain the gracious welcome to lesbian and gay people that the draft of the report included".
However, it said the synod's "openness to discussion provides hope for further development down the road".
Another group, DignityUSA, said: "Unfortunately, today, doctrine won out over pastoral need. It is disappointing that those who recognised the need for a more inclusive Church were defeated."
'A huge achievement'
Pope Francis prays as he opens the morning session of a two-week synod on family issues at the Vatican, 18 October 2014 Although Pope Francis' proposals were rebuffed, they still gained more than 50% of the votes
Correspondents say the text welcoming gay people and remarried Catholics had been watered down in the final version that was voted on - but it appears that they still met with resistance from conservatives.
All other parts of the draft report were accepted by the synod.
Christopher Lamb, from British Catholic journal The Tablet, told the BBC that the discussion at the synod was "a huge achievement in itself".
He said it was important to remember that many of the bishops at the synod were from countries where homosexuality is illegal.
"We have now got an acceptance that we need a new language in the Church when talking about gay couples and homosexuality in general," he added.
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Analysis: David Willey, BBC Vatican correspondent
Voting figures for the final document at the end of the synod show that Pope Francis received a rebuff in his attempt to persuade Church leaders to support his more merciful attitudes towards gay and divorced people. However, more than half still voted in favour of his proposed reforms.
Three crucial paragraphs in the final document all received more than 50% of the vote, although they failed to get the necessary two-thirds majority.
This allows the necessary leeway for further discussion before the synod reconvenes in Rome in an expanded form in a year's time.
Paragraph 55 of the final report, which has been rewritten many times during the past week, insists that although there can be no analogy between same-sex unions and marriage between a man and a woman, "men and women with homosexual tendencies must be welcomed with respect and delicacy".
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Speaking after the vote, Pope Francis told attendees that he would have been "worried and saddened" if there had not been "animated discussions" or if "everyone had been in agreement or silent in a false and acquiescent peace", AP news agency reported.
He also cautioned against "hostile inflexibility, that is, wanting to close oneself within the written word, and not allowing oneself to be surprised by God".
The earlier draft had said that homosexuals had "gifts and qualities to offer to the Christian community".
Bishops and Cardinals attend a morning session of a two-week synod on family issues at the Vatican, 13 October 2014 The synod has revealed divisions in Church opinion over how to approach family issues
Conservative groups had described the earlier draft as a "betrayal".
Cardinal Wilfrid Fox Napier of South Africa told Vatican radio on Friday that "there were two issues that got people 'hot around the collar'. One was presenting homosexual unions as if they were a very positive thing."
The second issue related to broken marriages "and the fact that people should be facilitated to get access to the sacraments", he added.
Following the synod vote, the revised document only said that discrimination against gay people "is to be avoided".
Appeal to traditionalists
The Pope said the full draft document, including the rejected paragraphs, should be published.
"Keep in mind this is not a magisterial document….the Pope asked for it to be made available to show the degree of maturity that has taken place and that which still needs to take place in discussions over the coming year," Holy See press officer Tom Rosica said on Vatican Radio.
The two-week synod has revealed a fracture line in church opinion over how to adapt traditional church teaching on human sexuality towards 21st Century attitudes, says the BBC's David Willey in Rome.
Pope Francis had made a powerful appeal to traditionalists not to lock themselves within the letter of the law, but conservative cardinals and bishops carried the day at the end of the synod, our correspondent adds.
About 200 bishops had attended the two-week synod on family issues at the Vatican.
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