Sydney Thunder star Kaur produced one of the all-time great World Cup knocks in the sudden-death semi-final, smashing an incredible 171 not out, seven bruising sixes and 20 boundaries as India piled on a rain-reduced 4-281 from 42 overs.

Australia lost three quick wickets at the outset including injured captain Meg Lanning for zero, and ultimately they fell 36 runs short after veteran Alex Blackwell's valiant efforts to produce a miracle chase came to an end.

"Our start with the ball was good, we executed our plans pretty well but ran into someone who was red hot and weren't able to adapt quick enough," Australian coach Matthew Mott said.

"It was probably the innings of her life but that is two we've had in this competition and not reacted well too - it's disappointing. They scored 40 or 50 too many, we needed to stop the hemorrhaging there when they were going and needed some discipline and it went to custard and they scored too many.

"They bowled extremely well to knock a few of us early. The ball was swinging and they hit the stumps which is what we we talked about doing.

"We left too much too late and needed some partnerships at the end and then could have come home like a wet sail at the end like they did."

Kaur's WBBL teammate Blackwell produced a magnificent 90 off 56 balls and put on 76 runs for the last wicket with Kristen Beams who came to the crease with 113 still required, but she was bowled by Deepti Sharma to end a superb game.

Much-maligned Elyse Villani had already done her best to pull Australia back into the contest and her agricultural and entertaining 75 was easily her best contribution of the tournament, but when she fell with the score at 126, India had control once more.

In the end this World Cup simply became too large a mountain to climb for Lanning's side, which managed six wins in the pool stage without ever finding their best form amidst Australian cricket's ongoing pay war which they must now return to as unemployed participants.

Lanning battled through a serious shoulder injury throughout the tournament and was rested two times during the group stage, most recently against South Africa last weekend.

When she came to the crease on Thursday with the score at 1-4 it was eight days since her last bat and she appeared bereft of the confidence that helped her craft 76 not out last week against India. She lost her off bail to Jhulan Goswami's without scoring - her first ODI duck in three years.

"It was a good ball, I think I could have played it a little bit differently, got a bit more forward to it," Lanning said.

"She was bowling really well up front there, her and [Shikha] Pandey I think, started off really well and put a lot of pressure on us. They didn't really give us any loose balls to go for which is what we were after.

"That put us on the back foot pretty early when they were able to get a couple of early wickets and we weren't able to get that platform that we were hoping to get.

What happens next with her chronic right shoulder injury remains to be seen, but she appears to be in doubt for the Ashes in Australia later this year.

The damage Kaur inflicted was crushing on the scoreboard, and soul destroying for Australia's toiling bowlers. They constantly picked three spinners throughout the tournament and Kaur took quite a shining to the tweakers, plundering her third 50 in just 17 balls at a speed the likes of Adam Gilchrist and Yuvraj Singh would've been impressed with.

When Australia dissects what went wrong in the semi-final, perhaps they'll decide they left themselves a seamer short against India, in a game where pace duo Sarah Aley and Belinda Vakarewa were both again left looking on from the sideline.

In fairness, no one in the world would have troubled Kaur on Thursday, and incredibly she helped India take 89 runs off their last six overs.

She wrote herself into the record books at Derby as the first Indian player, man or woman, to blast 150 in a knockout match at a World Cup.

Her score was the second highest ever by an Indian woman in ODIs - behind only younger teammate Sharma who hammered 188 against Ireland earlier this year.

It was also the second highest score against Australia, following on from Chamari Atapattu's 178 not out earlier in the tournament.

"I always love to play Australia, they are a very good side and when you score against a good side it's always gives you confidence," Kaur said.

"The WBBL, I really enjoyed it, I had a good team and they always gave me good confidence and my captain Alex is a motivating girl and she always appreciates my innings.

"For a cricketer it's always a dream to play at Lord's and we are really looking forward to that. It is a dream to play finals and hopefully we will do well there."

Amongst it all there was a bizarre moment when Kaur threw her bat in disgust at teammate Sharma, who she thought had been dismissed when hesitating before scampering through for the second run that brought up the century.

The third umpire deemed Sharma had made her ground, and Kaur swiftly retrieved her bat before celebrating a third international hundred and apologising to her colleague.

James Buckley is in England covering the ICC Women's World Cup as a guest of Cricket Australia.