Senators voted down the legislation 39 to 29 after hours of debate, CNN reported.
"I want to be very clear about the role of this expert group," Gillard said. "This expert group will receive the facts from government and beyond. They will be able at their option to receive briefings wherever they want to get those briefings from. They will be able to assemble all of the material to help them form their views. They will be able to consult as they see fit."
If the Migration Legislation Amendment (The Bali Process) Bill had passed it would have allowed Australia to send asylum seekers to Malaysia and the island of Nauru in the South Pacific for processing.
The bill was prompted by the sinking of two boats packed with people en route to Australia.
"The government could, today, have taken the pressure off these desperate people to get on boats by immediately resettling thousands of people waiting in Indonesia and Malaysia, properly resourcing the [U.N. High Commissioner for Refugees] and increasing search-and-rescue capability," Greens Sen. Sarah Hanson-Young said in a statement.
2014: The Year in Music [PHOTOS]