Brandis described Prakash as a "very important, high-value target".
He was actively involved both in recruitment and in encouraging domestic terrorist events in Australia.
"He was the principal Australian reaching back from the Middle East ... in particular to the terrorist networks in both Melbourne and Sydney. He was the person of greatest concern to us."
Senator Brandis said Australian authorities were instrumental in providing US allies with information about Prakash and his location in Mosul.
Shadi Jabar and her husband Abu Saad al-Sudani, who was also killed in the air strike, were actively involved in the recruitment of Australians to Isis, he said.
The latest advice from the nation's domestic spy agency ASIO is that about 110 Australians are in the Middle East as foreign fighters with Isis or engaged in its network.
Counter-terrorism expert Professor Greg Barton said Prakash was more a mouthpiece for Isis rather than one of its masterminds.
But his death was very significant nevertheless because Prakash was linked to a failed Anzac Day terror plot in Melbourne and the shooting death of NSW police worker Curtis Cheng in western Sydney last year.
"The fact that he's out of the picture is very welcome, but unfortunately there's many others there as well," Barton told Sky News. "A major breakthrough, but a long way to go."
The death of Prakash had degraded Isis' ability to recruit vulnerable people to conduct terrorist acts, Brandis said.
Prakash had appeared in Isis propaganda videos and magazines and recruited Australians, including children, and encouraged acts of terrorism.
"These incidents remind us that Australians who engage in terrorist activity and move into overseas conflict zones are placing themselves and others at significant risk."
- AAP
