Diplomatic ties have hit a low point in recent years as a result of the executions of two Australian drug smugglers, asylum seeker boat turn backs, a spy scandal and disruption to the live cattle trade, with both countries at different times withdrawing their ambassadors.
"We have not yet built the broader constituencies that would give the relationship genuine resilience," Department of Foreign Affairs and Trade secretary Peter Varghese said in a speech to the Australian National University Indonesia Project 50th anniversary celebration in Canberra.
Indonesia was a nation of "first order strategic significance" to Australia, he said.
However, outside of academic and government circles, there needed to be stronger business and community links that gave the "relationship the ballast it needs to cope with momentary political crises or differences in policy".
"The truth is Australia and Indonesia still face an immense gap in community awareness and understanding."
Mr Varghese noted there was some small elements of Australia-phobia in Indonesia, with outdated perceptions still persisting on such things as the White Australia policy.
Likewise, in some Australian quarters there was misunderstandings about the northern neighbour and a lack of awareness about its successful transition from dictatorship to democracy.
Mr Varghese pointed to a recent Lowy Institute poll which found Australians feel as warm towards Indonesia as they do to Russia.
Nevertheless he sees huge scope to improve on an undercooked economic, investment and commercial relationship.
This comes as projections place Indonesia as the fourth largest world economy by 2050, up from its current rank of 16th.
Indonesia's economy is expected to surpass Australia's by 2030.
Australia's education sector would be a big winner from Indonesia's burgeoning middle class, Mr Varghese said.
But he warned both countries must "resist the siren calls of protectionism and economic nationalism".