Somdev lost the first reverse singles 4-6 2-6 5-7 to his world number 18 rival in two hours and 44 minutes as India conceded an unredeemable 1-3 lead against the top seeds and defending champions in the first round tie.
India will now compete in the play-offs to enter the elite-16 nation World Group while Serbia have advanced to the quarter-finals.
Nevertheless, it was a brave-heart performance by the Indian players in the absence of veterans Leander Paes and Mahesh Bhupathi as they made formidable Serbians work hard to win the tie.
Somdev did extremely well by beating Janko Tipsarevic on the opening day but losing yesterday''s doubles rubber cost India dearly.
Today, it all depended on Somdev to keep India''s challenge alive by drawing parity in the tie but Troicki punctured the hopes of the visitors with a clinical show before the home crowd.
If Troicki was confidence personified, Somdev was not even the pale shadow of his usual fighting self once he surrendered the opening set, though he fought hard in the third set.
As if loss of form was not enough, poor umpiring added to the frustration of Somdev as yet again scenes of arguments with the chair umpire were witnessed.
In the sixth game of the third set, Somdev refused to continue the match over a doubtful call and the match referee had to intervene and convince the incensed Indian to resume.
Troicki hit a shot near the baseline at 40-30 which looked going out but umpire ruled the point and thus game in favour of the Serb.
Somdev first argued and then refused to continue but the match referee eventually succeeded in continuing the game.