Llanelli crashed out of the Intertoto Cup on away goals despite a remarkable second leg win in Carmarthen on Sunday.
Trailing 3-1 from the first leg, the Reds looked down and out when Vetra took a fourth-minute lead.
Llanelli hit back to go 2-1 ahead, but the Lithuanians struck twice in four minutes before the break to lead 3-2.
Rhys Griffiths levelled on 58 minutes and added another two to secure victory on the night, but time ran out as Llanelli pressed for the vital sixth.
The Reds, playing at Carmarthen's Richmond Park because their Stebonheath Ground does not meet the required Uefa standard, made a horrendous start by allowing Vetra to score on their first attack.
Brazilian Lima Severino converted a low cross to leave Peter Nicholas' side with an even higher mountain to climb.
But the fightback began in the 18th minute when Vetra goalkeeper Stanislav Kozyrev turned the ball into his own net from Andy Legg's long throw.
Legg, signed just a few days ago to add experience to the Llanelli ranks, was the architect of the second too as another long throw caused chaos and Wyn Thomas headed home.
Back came the visitors, though, as Vitalis Stankevicius scored from the penalty spot on 43 minutes after a Antonio Corbisiero handball.
And they regained the lead on the stroke of half-time when Egidijus Juska scored from a well-worked free-kick.
Last season's Welsh Premier top goalscorer Griffiths scored his first 10 minutes into the second half and then completed his hat-trick with two late strikes - the last from the penalty spot in the last minute - to ensure a 5-3 victory.
The Reds threw everything at Vetra in the four minutes of stoppage time, but the visitors held on to go through having scored two more away goals.
Vetra now take on Polish outfit Legia Warsaw in the second round, with the winners facing Blackburn Rovers in the next round in August.
Llanelli: Harrison, Legg, Lloyd, Corbisiero, Jones, Thomas, Williams, Mumford (Wanless 69), R. Griffiths, Blackman (Follows 76), Small.
Subs Not Used: Dale Griffiths, Thompson, Darren Griffiths, G Williams, Clark.
Goals: Kozyrev 18 (og), Thomas 40, Griffiths 55, 88, 90 (pen).
Yellow cards: Lloyd (90).
Vetra: Kozyrev, Botelho, Budimir, Skerla, Usaciov, Panka (Butrimavicius 78), Bozinovski, Juska (Azizi 72), Severino, Miloseski (Karcemarskas 58), Stankevicius.
Subs Not Used: Kacinkevieius, Birakys, Celiuk, Grigaitis.
Goals: Severino 4, Stankevicius 43 (pen), Juska 45.
Yellow cards: Miloseski 44, Azizi 90, Kozyrev 90, Skerla 90.
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