Image copyright AFP Image caption Many Japanese reacted on social media after the game saying they had nothing but appreciation

Japanese fans who watched their team play the US in the Women's World Cup final on Monday on their commute or followed on social media were disappointed by their loss, writes the BBC's Yuko Kato in Tokyo, but also full of respect and appreciation.

Immediately after the game, former Manchester United player and member of the men's national team Shinji Kagawa said it all, tweeting: "Thank you for always being so courageous. You make me proud as a fellow Japanese. To everyone in Nadeshiko Japan, thank you so much for your hard work."

Nadeshiko - a pink flower often associated with the traditional concept of Japanese female virtue - has been the team's nickname since 2005.

Kana Ohyama, a former national volleyball player tweeted: "Every Nadeshiko is just too fabulous. Too awesome."

Writer and editor Yumi Toyozaki tweeted: "The U.S. was a really good team. Well done, Nadeshiko. Thank you for bringing us along all the way to the finals!"

Image copyright AFP Image caption The Japanese national team won the Women's World Cup four years ago

Another fan, azukKI, tweeted: "People on my feed are more moved than disappointed, and I'm welling up."

She also echoed another popular sentiment among Japanese fans: "Everyone was so cool, so awesome. Everyone was like Furiosa. #MadMaxBrain."

The film Mad Max: Fury Road is becoming a bit of a cult phenomenon in Japan, especially on social media, and so the sight of tough and capable women fighting their hearts out on the football pitch seems to have caught the imagination of people.

Love and support

The Nadeshiko Japan had a tough act to follow: themselves.

The 2011 women's football World Cup in Germany took place just four months after the earthquake and tsunami that devastated parts of the country, and the subsequent Fukushima nuclear disaster.

Many people were downcast amid a daily barrage of reports about death, radiation, and fear for the future.

Image copyright AFP Image caption Homare Sawa, the captain four years ago, rejoined the team this year

But then the Japanese women played their hearts out, against a much bigger, stronger US team. They just kept running and running, and then won.

By doing so, they secured a special place in the hearts and minds of the Japanese public, and the love and support was rekindled by their advance this time.

Homare Sawa, who was the captain four years ago, was named the 2011 Fifa Women's World Player of the Year, and since then has become a national hero.

She re-joined the national team at the last minute in May, and this World Cup was said to be her last.

The expectation and sense of trust when she entered the game in the second half was palpable on social media.

Football illustrator @riota2gaoe tweeted an image of Sawa that captured the country's imagination after the victory four years ago.

Image copyright @riota2gaoe

Former team-mates commented from the public broadcaster NHK's studio "now everyone will be watching her".

The image of Japan's legend Sawa tackling America's legendary player Abby Wambach was met with oohs and aaahs; seeing them shake hands and embrace after the match also made many fans extremely emotional.

Women's football in Japan first gained national recognition in the 2004 Athens Olympics.

They gained much attention when they reached the semi-finals in the 2008 Beijing Olympics, which was also fought and lost against the Americans. And in 2011, they became national heroes.

Image copyright AFP Image caption Japan has fewer female football players than the US or the UK

There are two women's football leagues in Japan with 32 teams. They are popular locally and enjoy a close relationship with the community, but only a handful of players are fully professional.

According to the Japan Football Association, in 2013 there were 30,000 registered female football players in the country.

In contrast, the US in 2007 had 1.7m registered female players. In England, according to The Football Association, as of September 2014, there were 2.6m women and girls playing football.

Some pundits say the reason the Japan national team does well is precisely because not many girls and women play football and therefore they lack the opportunity to be in a strong female team during school.

Those girls that are really passionate about playing football will often have no other choice but to practice and compete with boys and men, which is how the previous captain Sawa and the current captain Miyama trained during primary and secondary schools.

And their stories became widely known after their 2011 victory.

A popular manga (comic) series by Akimi Yoshida called, Umimachi Diary (Sea Town Diary), which has been turned into a film with the English title Our Little Sister, features a teenage girl who plays football in a boys team.

Image copyright AFP Image caption Umimachi Diary is now a feature film, starring Masami Nagasawa, Suzu Hirose and Ayase Haruka

She is actually much better than the boys, and has to deal not just with family issues and the usual teenage issues, but also figure out if she really is passionate enough about football to try and become a serious player.

The comic series is still being written in a monthly magazine and whether or not the little sister, Suzu, decides to pursue football is a major plot line, so no spoilers here.

Nevertheless, the image of the Nadeshiko yet again fighting and running till the very end, gaining the respect of their peers, may inspire young girls like Suzu around the country to think, yes, this is what I want to do.