Fresh from their historic gold medal winning feat in World Cup Stage I in Shanghai, the men's compound team lost to second seeded Danish team 234-236 in a tight battle.
Locked 117-all at the midway stage, the women's team faltered under pressure to lose to top seed Denmark 230-233.
The men's and women's teams will now battle for bronze medals against France and Italy respectively on June 10.
There was heartbreak in store in the recurve section as well where men's team made a first round exit going down to lower ranked Germany 0-6, while in the women's side lost 0-6 to Russia in the quarterfinals.
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The sixth seeded trio of Abhishek Verma, Chinna Raju Srither and Gurwinder Singh had no answer to the Danish team's superlative show as they started off with a 58.
Indians matched their Danish opponents in the remainder three ends but it was not enough as the two-point lead in the first end clinched the issue.
All eyes will now be on top seed Deepika Kumari in the women's individual section where she and unheralded Monika Saren will be seen in action tomorrow as two other Indians, Preeti and Ankita Bhagat, made round two exits.
Monika, who is seeded 31, got a first round bye and went on to beat 34th seed Anastasia Pavlova of Ukraine 7-3. She will face a tough challenge from second seed Peng Chia-Mao of Chinese Taipei in round three.
45th seed Preeti started with promise defeating Astrid Daxbock (68) of Iceland 6-0 but went down to 20th seed Ana Umer of Slovenia by an identical margin.
Seeded 49, Ankita defeated Karakoz Askarova (64) of Kazakhstan 6-0 before losing to 16th seed Lin Shih-Chia of Chinese Taipei 3-7.
Seventh seed Dhaniram, who got a bye into round three, will face 26th seed Arsalan Baldanov of Russia.
Beginning his campain from round two, 13th seed Das defeated Miguel Pifarre Trujillo of Spain 7-3 and will face Muhammad Akmal Nor Hasrin of Malaysia tomorrow.
Swami began with a 6-0 win over Levon Poghosyan of Armenia before going down to Onur Tezel of Turkey 4-6.
In the men's compound individual section, Verma beat 55th seed Gudmundur Orn Gudjonsson of Iceland 146-126.