The Alliance proposal, brought by Councillor Peter Lavery and seconded by Councillor Eóin Tennyson, would have seen the Council write to Environment Minster Edwin Poots to call for a ban on the practice.
Members of the DUP, UUP and SDLP voted to oppose the proposal.
Expressing his disappointment, Councillor Lavery said: "Fracking has a devastating impact on the local environment, so it is important we take every opportunity to oppose this outdated practice.
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"There is also clear precedent for Council taking such stances and lobbying the Executive on planning matters. Earlier this year, we wrote to Infrastructure Minister Nichola Mallon to raise concerns with a Planning Advice Notice relating to development in the countryside. There's absolutely no reason why we could not lobby in a similar manner on this important issue, especially as multiple Councils have already taken similar stances."
Councillor Tennyson added: "We regularly hear rhetoric and platitudes in relation to climate change, but unfortunately when the issue came before Council, the DUP, UUP and SDLP failed to step up to the plate and take the necessary and courageous action required.
"Residents of our borough can be assured Alliance will continue to oppose the destructive practice of fracking and work towards a greener, more sustainable future for everyone."
