Harmanpreet Kaur's side lost to the defending champions by 85 runs in front of more than 86,000 fans -- a record attendance for women's cricket -- at the Melbourne Cricket Ground on Sunday.
Despite the defeat it was a successful World Cup for the team, who reached the final for the first time and whose star batter, 16-year-old Shafali Verma, moved to the top of the world rankings during the tournament.
Indian cricket chief Sourav Ganguly praised the women for making the final, a month after the men's under-19s were runners-up in the 50-over World Cup.
"Well done the Women's team @bcci @JayShah .. (After the Under-19) Two back to back World Cup finals .. but we lost," Ganguly tweeted.
"We're super .. we will get there someday .. love the team and players."
Men's captain Virat Kohli said he was "proud" of the women, who went into the final unbeaten and had outplayed Australia in the opening game of the tournament.
"Proud of all the efforts put in by the Indian Women's Cricket Team throughout their #T20WorldCup campaign. I'm confident that you girls will bounce back stronger than ever," Kohli tweeted.
Nothing went right on Sunday for India, who lost the toss and then watched as Verma dropped Alyssa Healy in the first over.
Healy went on to smash 75 off 39 balls to get the player of the match award.
Australia marched to a record fifth women's T20 World Cup title after posting 184 for four. India were sent packing for just 99 in reply.
"It was a tough day for #TeamIndia. Our team is young and will grow into a solid unit. You have inspired many across the globe," retired batting superstar Sachin Tendulkar wrote on Twitter.
"We are proud of you. Keep working hard and never lose hope. It will happen one day."
A teary-eyed Verma was consoled by her team-mates as she left the field. Kaur said the young team had a bright future.
"In the last T20 World Cup we reached the semis and this year in the finals. If we keep working and improving then in the future we will win," said Kaur.
"You see our team is quite young. Young girls are coming and giving a 100% for the team. And I think this (making the finals) will motivate many girls back home and they will come and play cricket." - AFP
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