Natasha was beaten by Belarussian rival Sviatlana Pirazhenkha in straight sets, while Karman also went down in straight sets to Japan's Ayaka Okuno.
Natasha lost the opening set easily and then she regrouped a bit to offer some resistance. She took the second set into tie-break, which she lost 3-7.
Karman Kaur committed nine double faults to just two by Ayaka Okuno of Japan to hand over the initiative to her opponent.
India's top women's singles player Ankita Raina, seeded fourth, will be seen in action tomorrow as she takes on another qualifier - compatriot Rutuja Bhosale - in round one.
More From This Section
Also in fray tomorrow is Sharrmadaa Baluu, who has drawn Ukrainian top seed Anastasia Vasylyeva, ranked 172 currently, as her first round opponent.
The results:
Singles (1st round): Ayaka Okuno (JPN) beat Karman Kaur Thandi (IND) 6-2 6-4l Despina Papamichail (GRE) bet Miki Miyamura (JPN) 6-2 4-6 6-3; Katy Dunne (GBR, 6) beat Anna Morgina (RUS) 7-6(7) 6-7(1) 6-4l Magdalena Frech (POL) beat Manon Arcangioli (Fra, 5) 6-1 6-2; Polina Leykina (RUS, 7) beat Jia-Jing Lu (CHN) 3-6 6-3 6-4; Kamonwan Buayam (THA) beat Kamila Kerimbayeva (KAZ) 7-5 6-4; Ellen Allgurun (SWE) beat Miyabi Inoue (JPN) 7-6(2) 6-3; Sviatlana Pirazhenka (BLR) beat Natasha Palha (IND) 6-0 7-6(3).