Kom, 29, had to settle for bronze along with the other losing semi-finalist after she was beaten 11-6 by Britain's fancied world number two Nicola Adams in the 51kg category on Wednesday.
The boxer, who won five world titles in the 46kg and 48kg categories, had to move up a weight category to fight in London since her favoured events were not part of the inaugural Olympic competition in women's boxing.
Sports Minister Ajay Maken congratulated the tiny boxer from the north-eastern state of Manipur, who took up sport as a path out of poverty.
"Mary Kom playing in a higher weight category, played well but lost to a taller/younger/stronger player," Maken wrote on Twitter. "Olympic bronze is also a big achievement."
Kom's medal ensured India will return from London with its biggest Olympic haul, surpassing the one gold and two bronzes it won in Beijing four years ago.
India has so far won a silver through pistol shooter Vijay Kumar and three bronze medals by badminton star Saina Nehwal, rifle marksman Gagan Narang and Kom.
Bollywood legend Amitabh Bachchan and cricket superstar Sachin Tendulkar also paid glowing tributes to Kom.
"My great honor and privilege to have spoken to Mary Kom earlier today on the phone," Bachchan tweeted on Wednesday night. "What a lady!! You have made all of India proud!"
Tendulkar tweeted: "Mary Kom is an amazing woman. What an effort to win a medal for India. We all are extremely proud of you."
The Indian media, whose sports coverage is normally focused on cricket, hailed Kom's achievement on the front pages.
The Indian Express said she won a "bravery medal in guise of an Olympic bronze", while the Hindustan Times headlined its report "Mary loses, wins hearts and bronze."
Prime Minister Manmohan Singh, in a message to Kom, said: "Our medallists have done us proud during these Olympic Games. I hope their achievements will spur a new generation of sportsmen."
India is hoping to garner more medals from its wrestlers, including Beijing bronze medallist Sushil Kumar, when the competition begins later on Thursday.