Moscow on Wednesday vetoed a move to establish a special tribunal to try those responsible, while Angola, China and Venezuela abstained.
Eleven of the 15 members of the Security Council voted in favour of the resolution, drafted by Australia, Belgium, Malaysia, the Netherlands and Ukraine.
All 298 passengers and crew on board the Boeing 777 were killed when the Malaysia Airlines plane was blown out of the sky over Ukraine during a routine flight between Amsterdam and Kuala Lumpur on July 17 last year.
Moscow denies involvement and blames the Ukrainian military.
"We are absolutely determined to provide answers to those families," Foreign Minister Julie Bishop told Channel Seven of those who died.
The victims were mostly Dutch but included 38 Australian citizens and residents.
"The five nations - the Netherlands, Malaysia, Belgium, Australia and the Ukraine - are determined to continue to find an alternative mechanism.
"We will be meeting again shortly and we will come up with a way that will hold the perpetrators of this atrocity to account."
"Of course, we're doing this for the families, but the broader international community, civil aviation must be seen to be safe," she said.
"People must be able to put their faith and their trust in commercial airlines and travelling on commercial planes.
"And so, we need to send a very strong message to those responsible for this that they can't hide, that they will be held to account and they will be able to present their response to a court and a court will hold them to account."
But Bishop said the reaction raised more questions than answers.
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