Nyambayar, who was a world silver medallist in 2009, defeated the Beijing 2008 Olympic Games bronze medallist 17-16 in the men's Fly Weight last 16.
Though Picardi took the first round 6-4, the Mongolian fighter took control of the bout using his impressive upper cut and claimed the next two rounds 6-4 and 7-6.
Picardi, although visibly disappointed by the defeat, was quick to acknowledge the quality of his opponent.
'I'm not going to complain about the results,' he said. 'The Mongolian's a champion as well.
'I should have fought differently.'
Top-seeded Russian Misha Aloian secured an easy win as he beat Samir Brahimi from Algeria 14-9, claiming every round.
There was also a win in the Fly Weight division for Jeyvier Cintron Ocasio against Juliao Henriques Neto while Jasurbek Latipov made short work of Hashem Abdelaal.
In the men's Welter Weight category, reigning world champion Taras Shelestyuk defeated Moldova's Vasilii Belous 15-7 as he dominated from start to finish.
Nyambayar's Mongolian compatriot Tuvshinbat Byamba went down fighting against Frenchman Alexis Vastine in a close bout which ended 13-12.
Custio Clayton of Canada defeated Australian Cameron Hammond 14-11 while home favourite and world number two Freddie Evans concluded the session by defeating Lithuania's Egidijus Kavaliauskas 11-7.