Exceptional work by the Indians. I'd give each of the bowlers the MOTM award for the way they rose to the occasion, consisting mainly of debutants and the most experienced with only two (or thereabouts) test matches to his name. Fantastic efforts.
From Australia's point of view, there are some structural, management and player issues that need to be addressed.
The holiday for the Sheffield Shield during the test series is the first and perhaps main issue. Just no way of getting out of form players back to their best, or for gauging the form of potential replacements. To illustrate, Joe Burns was seriously out of form from the beginning, but he had no opportunity to go back to SS to rectify his problems. His replacement was Marcus Harris who had been in good to very good form early in the Shield, but had not played for some weeks before being required to take over the opening duties from Burns. His lack of recent game time I believe was on show.. Similarly, Warner would have benefited from a couple of first class games before being recalled. The other player completely out of form was Mitch Starc. But he also had no opportunity to get fit, overcome injury or whatever the problem was while no other bowler had the opportunity to show form at Shield level to come into consideration.
Poor management, team tactics and a failure to maximise opportunity also came into play. We have at least a couple of batsmen (Harris and Head) who have displayed the same failings at test level over a number of years and there is no discernable evidence that they are getting any help to overcome their deficiencies. Management also fell down in the area of selections. After the win in Adelaide, Justin Langer was quite outspoken about not changing a winning team even in the face of a few very poor efforts by players in that match. That win, and the massacre in the Indian second innings seemed to form a belief in the team management that we had the Indians on toast for the remainder of the test season. Very poor judgement to base decisions on an Aussie win with the pink ball under lights where we are practically unbeatable in those conditions. Further, the decision to bat first in Brisbane was a mistake which handed the Indians the opportunity to dictate how the game would pan out. Australia needed to win that test to win the series. India only needed not to lose to retain the Border/Gavaskar trophy. They held all the cards when it came to options to bat out for a draw or go for a win in the second innings. The way they managed their run chase is also a salutary lesson for the Australians. Note how Smith and Labuschagne started chasing fast runs from the moment they came to the crease in the second innings and the early downfall of Marnus as a result. These were precisely the players who should have got in before taking to the bowling. Field placings by Tim Paine, probably with input from Langer, were defensive and poor in comparison with the Indians; as a result both Indian spinners, including one having I think his first test match were more dangerous and successful than our GOAT, Lyon. Although, Lyon really needs to add much more variety to his repetoire to be regarded as a high quality test spinner, especially against sides like India who thrive on spin.
Many other issues, but that will do for the moment. My first action if in a position to do so, would be a change in the coaching setup and adoption of a more attacking mindset in game tactics and fielding positions.