Kohli magic almost enough for India

India's stand-in skipper Virat Kohli says it's the greatest game he's played in.

But he's more than happy to hand the captaincy back to MS Dhoni for the next Test.

Kohli led a bold run chase on Saturday's gripping final day of the first Commonwealth Bank Test in Adelaide, but India ultimately fell 48 runs short.

Kohli's highest Test score, a sublime 141, raised hopes of an incredible Indian win, becoming just the fourth Indian to score centuries in each innings of a Test.

"If we were able to pull this off, today would have been one of the most special moments in my life," Kohli said.

"But I'm really proud of the way the boys played."

Kohli wasn't disappointed, just "a little bit hurt because of the fact that we couldn't cross the line when it looked pretty bright for us".

At no stage did the tourists consider batting for a draw, despite being set a daunting 364 runs to win on the last day on a wearing pitch.

"At no point did we back off. And we are not going to back off either," Kohli said.

"If you see cricket like this for the rest of the series, it's in the balance. The guys are believing that.

"And unless you believe in something, there's no chance of achieving it.

"If at any stage that we had in mind that we might play for a draw, we would have lost by 150 runs, to be honest.

"So we went for it. That is what I am happy about."

Dhoni, who missed the series opener because of a fractured thumb, will return to the captaincy for the second Test in Brisbane starting Wednesday.

"I would be very happy that he is going to be fit and available for the second Test," Kohli said.

"It doesn't matter if I have the 'c' in front of my name or not. That doesn't change anything as far as my mindset is concerned.

"I have enough friendship and enough respect between the team that I can go and speak to them every now and then and keep them on the same page.

"That is my responsibility, that is something I will look to do even if I'm not captain."