The marathon match stretched for three hours and 47 minutes at Court 9 here on Monday.
Myneni, ranked 143rd, fought bravely for the better part of the match despite conceding the first set in a tie-breaker.
He responded strongly to the setback, playing aggressively to break his opponents serve thrice to claim the next two sets to raise hopes of victory against his 49th ranked opponent.
But his movements were severely restricted by cramps that forced him to concede the fourth set.
But that didn't deter the 28-year-old Visakhapatnam based right hander from battling on and was leading 4-1 in the deciding final set.
Both players were relentless and waited for the opponent to falter.
But Vesely, five years his younger, and aided by Myneni's cramps, utilised the opportunity holding his nerve to break the Indian thrice consecutively to recover from 2-5 to win the set.
Once he pulled level at 5-5, the left-handed Vesely went for the kill and broke Myneni's serve again to close out the final set 7-5. In the end, Myneni could barely stand due to physical exhaustion.
Myneni was the sole Indian in the men's singles competition. He is the first Indian since Yuki Bhambri to enter the main draw of a Grand Slam event and also the first since Somdev Devvarman in 2013 to qualify for the US Open main draw.
Myneni won three qualifying rounds without dropping a set to enter the main draw of the US Open.
He outplayed Pedja Krstin of Serbia 6-3, 6-0 in the third and final qualifying round on Saturday. He did not drop a set in the three rounds of the qualifying event.
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