Australian captain Tim Paine insists he is the right man to lead his team to South Africa and to the possible Test championship final at Lords despite a sub-par performance in the Test series against India.

India beat Australia by three wickets at the Gabba on Tuesday, the first time since 1988 the Australians have lost a Test in Brisbane.

The win ensured the tourists claimed the series 2-1 and retained the Border-Gavaskar Trophy they won in Australia in 2018-19.

Paine conceded he was below par in the last two Tests.

He dropped a number of chances on the final day in Sydney, when India batted all day to salvage a draw, and missed a stumping on the last day in Brisbane as Rishabh Pant led India to a stunning victory.

Paine also came under heavy criticism from a number of former players over his bowling changes, field placings and his decisions on when to declare.

But he said that he had no intention of stepping down and would take Australia to South Africa in February.

"I'm still looking forward to going to South Africa to try and win a series there," Paine said.

"We had a goal to make the Test championship final -- that's still achievable and it's a goal for me and the group."

India are now top of the Test championship table, with New Zealand second and Australia third.

The series against South Africa is the last chance Australia have of reaching the top two and making the August final at Lords.

Paine was also forced to fend off criticism from former Australian great Adam Gilchrist that he couldn't captain effectively and keep wicket as well.

"I think I had an ordinary day in Sydney, I'll cop that on the chin," Paine said.

"It doesn't always go your way in cricket or in life so for me it's about soldiering on.

"I said a few times I have improvement in me, I still feel like I want to get better and I certainly want to keep leading this team."

Paine was appointed captain and wicketkeeper after the ball tampering scandal in South Africa, which led to Steve Smith being stood down as captain and suspended for 12 months.

"I'm loving the job. I'm going to cop heaps of flak I know that," he said.

"I've been absolutely belted by the Indians over the last seven days -- that's been interesting.

"But that's par for the course for this job."