Britain needed to beat the world number one-ranked side to tie the series having drawn 2-2 in the opener before losing the second Test 4-3.
Australia legend Jamie Dwyer, 37, scored twice in his last home Test, including the final goal.
Simon Mantell had cancelled out Dwyer's opening goal with a close-range effort to make it 1-1.
However Australia then pulled clear as they scored through Simon Orchard and Blake Govers, following penalty corners, and a Mark Knowles penalty stroke to lead 4-1 after the third quarter.
GB head coach Bobby Crutchley said: "It's very tough to beat the top teams in the world when you gift them goals.
"Our deep defence was not as strong as in recent games and after conceding the third it was always going to be tough getting back in the game."
The teams will meet again on the opening day of the Champions Trophy in London on 10 June, and are in the same pool at the Rio Olympics in August.
Australia comfortably defeated Great Britain 5-1 in the final Test in Perth to complete a 2-0 series win.