The incident was the first confirmed fatal shooting by foreign peacekeepers since they arrived in the East Timor last June.
There has been a recent surge in violence ahead of presidential elections in April.
Peter Lindsay, Australia's defence secretary, told ABC's Radio Australia on Monday: "Frustrations were clearly boiling over at the airport and we've seen this unfortunate two deaths now.
"Our troops operate on very strict rules of engagement. They will never fire unless they're operating under those rules and unless they're physically and personally threatened.
"There will be a full investigation, we'll get to the bottom of that with a view to try to make sure that circumstances are such that we can mitigate that in the future."
At one point, Monday's funeral procession headed along Dili's main road towards the heavily fortified Australian embassy.
Portuguese police, here under the UN peacekeeping mission, diverted the march, managing to avoid any clashes.
MacDonald said: "The anger being displayed here today is symptomatic not just the anger over the shooting incident, but also growing resentment towards the international security presence here in East Timor."
Agosta Dacosta Soares, one of the victim's brother, told Al Jazeera: "You can ask everyone here, we all want the Australian troops out."
Lindsay said there were no plans to withdraw soldiers from East Timor.
He said: "My understanding is we're going to be in Timor for a long time trying to help that very poor country establish itself and be a successful country."