Australia captain Tim Paine: We were outplayed in key moments against India

India wrapped up a 2-1 series victory after the fourth Test petered out in a draw at a rain-drenched Sydney Cricket Ground on Monday

Australia's captain Tim Paine, centre, watches on with teammates as India celebrate a 2-1 series victory following play being abandoned on Day 5 in the fourth Test match in Sydney. Reuters

Tim Paine said his Australia side were outplayed at key moments as they became the first home side to lose a Test series to India on Monday.

India wrapped up a 2-1 series victory, their first in 71 years of touring Australia, after the fourth and final Test petered out in a draw at a rain-drenched Sydney Cricket Ground on Monday.

It leaves Australia captain Paine, who assumed the armband in the wake of the ball-tampering scandal in South Africa last year, with just one win - last month's victory in Perth that tied up the series at 1-1 - in seven Tests at the helm.

Paine, 34, admitted his inexperienced side had been completely outplayed in the last two matches in Melbourne and Sydney but thought the series might have panned out differently had the Australians done better in the opener in Adelaide.

"We honestly feel that we let that Test match slip," he told reporters.

"We thought had a number of opportunities in that Test to get ahead of the game, and when those key moments came up, India outplayed us.

"More often than not when those big moments came up, Virat [Kohli] scored a century or [Cheteshwar] Pujara scored one or [Jasprit] Bumrah bowled a great spell and got them through those moments.

"Their best players stood up in the big moments."

Paine said the Australians needed to emulate the Indians when they take on Sri Lanka in a two-Test series.

"We can learn a lot from the way they went about it and we'll make sure we do," he said.

"We'll have a week off and get ready for the Sri Lanka series. We've got faith that the guys around the team are the right guys."

Paine said he had faith that senior batsmen Usman Khawaja and Shaun Marsh and the pace bowlers Mitchell Starc, Josh Hazlewood and Pat Cummins would rediscover their best form after under-par series.

He thought that opener Marcus Harris and Travis Head, who probably got their chances because of the absence of Smith and Warner, had acquitted themselves well at Test level.

Still, the numbers don't lie. Man-of-the-series Pujara hit centuries in India's victories at Adelaide and Melbourne as well as the drawn Sydney Test on his way to a series total of 521 runs no Australian batsman managed triple figures in an innings.

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"Clearly, we know we're not going to win too many any Test matches without scoring hundreds," he said.

"But when guys are in their third, fourth Test matches, it's hard. We had so many starts throughout this series, it's just the experience of learning how to convert them.

"[And the Indian] attack was seriously good. I don't think in Australia we've given them enough credit for how relentless they were. It was hard work batting even for seasoned test players."

After a one-day series against India, Australia next take on Sri Lanka in Brisbane starting on January 24 followed by the second Test in Canberra.