The Delhi boy's 3-6 5-7 2-6 defeat in sweltering heat in the must-win fourth rubber means that India will remain in the Asia|Oceania Group 1 for next year's competition while the top seeds and three-time Champions Czech Republic regained their place in the elite-16 nation World Group.
India needed Yuki to win to remain alive in the tie but the 23-year-old today lacked the required fighting spirit despite that the hot and humid conditions were bothering the left-hander.
The doubles loss for the fancied Leander Paes and Rohan Bopanna also hurt India's chances in the tie.
Since the fate of the two teams was sealed, the two teams decided not to play the dead fifth rubber between Somdev Devvarman and Lukas Rosol.
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India were trying to re-enter the World Group for the first time since March 2011 when they had lost to Serbia 1-4 in the first round.
Vesley dictated the terms in the two hour and 14 minute contest as he played the entire match on Yuki's backhand. And he served strong to wriggle out of a few tough situations.
The key to Vesley's success was that he played with lot of control. He committed only three unforced errors in the opening set and was rewarded with his first ever win in live singles rubber in Davis Cup.