The campaign group's speaking after the Labour Party blocked the ruling conservative coalition's attempts to vote a referendum on the issue through the country's parliament.
The coalition, which has varying views on same-sex marriage, believes Australians should be allowed to have their say on the issue. It needed Labour's support to get the referendum through.
The Labour Party says only members of parliament should decide, in order to avoid a potentially divisive debate regarding same-sex marriage.
If the referendum was voted through it would have taken place on 11 February next year.
The Australian Christian Lobby said it was disappointed "that ordinary Australians are being shut out from having a say about the biggest social policy change in a generation".
Labor Party leader Bill Shorten said: "This country does not have the right in a plebiscite to pass judgment on the marriages and relationships of some of our fellow Australians. It is not what Australia is about."
The ruling conservative coalition has urged Labour and other Australian politicians to allow citizens to have their say on the topic.
