Australia fear they might have let India off the hook on the first day of the deciding Test in Brisbane, according to centurion Marnus Labuschagne.

Number three Labuschagne reached three figures for the first time in the series with a typically diligent 108.

However, he top-edged a pull off debutant seamer Thangarasu Natarajan (2-63) to be pouched by wicketkeeper Rishabh Pant, shortly after Matthew Wade departed to the same bowler for 45.

Like Wade, Steve Smith was guilty of not capitalising on a start when he became Washington Sundar's maiden Test wicket on 36, although Cameron Green (28 not out) and under-fire captain Tim Paine (38no) got the hosts to 274-5 at stumps with the four-match series all square at 1-1.

"Look, all our batters are going to make their own assessment of the way they got out. They're all international players," Labuschagne said.

"You know everyone gets judged harshly. You're your own harshest critic and everyone will look at their dismissals and say, 'What could I have done better?'

"I'm definitely disappointed about not going on and getting a really big score that would have put us in a better position as a team.

"We'll still take the position we're in, it was really nice to see Greeny and Tim finish it off there when we did lose two wickets in quick succession."

Injuries have laid waste to India's plans over the course of the series and Natarajan and Sundar featured for the first time in the longest format as key men Ravichandran Ashwin and Jasprit Bumrah were ruled out.

It meant learning on the fly against unfamiliar opposition, although it was a challenge Labuschagne relished.

"Definitely I had to formulate some plans on the run and keep trying to understand the situation, what they were doing. That's the part of the game that is really enjoyable." he said when considering an India attack that was further compromised by the loss of Navdeep Saini to a groin injury after only 7.5 overs.

"You've got to read the situation out there. You can look at stuff on a screen and see how guys bowl but only you know out there, with a feel of how you can do things and how you can make things easier. "

Not for the first time, Smith was the centre of controversy for alleged gamesmanship on the final day of the drawn third Test, but Labuschagne failed to spot any ill-effects as the pair shared a stand of 70 for the third wicket.

"I don't think when he walks out onto the field that stuff really concerns him. He's focusing on the ball and scoring runs," he added.

"If anything it gives him extra motivation to put big runs on the board. I don't think that stuff comes into play when he's out there at all."