The Irish side went down by a 4-0 scoreline in Hungary, leaving them with the task of pulling off one of European football's greatest comebacks to earn a place in the group stages of this competition.
Match preview
Given their performance in the previous round and their current standing in Irish football, Shamrock Rovers would have been optimistic about pulling off a shock against Ferencvaros to progress further in the Europa League.
However, as they fell 2-0 behind inside 34 minutes, it became apparent that it was a step too far for Stephen Bradley's team, who also conceded a fourth in the final minutes.
Realistically, the tie was already over before that effort, but Shamrock can at least head into this game knowing that the consolation prize is an appearance in the Europa Conference League group stages.
Even though they gave their supporters reasons to dream of better, it remains a monumental achievement for a team who last experienced an extended continental run back in 2011-12, where they lost all six group-stage matches.
While Bradley may make changes to take the upcoming schedule into consideration, he will also want to build on the weekend's 3-0 victory over nearest rivals Dundalk, extending their lead to seven points at the top of the League Of Ireland Premier Division in the process.
Not so long ago, Ferencvaros would have had aspirations of earning a spot in the Champions League group stages, something which ended with defeat to Qarabag in the third qualifying round.
Facing a team like Shamrock was regarded as a potential banana skin, but having the chance to play the first leg on home territory gave them the chance to seize full control of the tie.
Adama Traore netted twice to take his recent tally to four goals from three appearances, and the Mali international will want to extend that streak on Thursday night.
Even though Stanislav Cherchesov's team were afforded a weekend off from domestic action and dropping two games behind some of the other teams in Hungary's top flight, they still sit in second spot after two successive victories.
Shamrock Rovers Europa League form:
Shamrock Rovers form (all competitions):
Ferencvaros Europa League form:
Ferencvaros form (all competitions):
Team News
Having only made a couple of changes for the dominant win over Dundalk, Bradley may be prepared to stick with the players who started that game.
Aaron Greene and Rory Gaffney both got on the scoresheet before their withdrawals on the 68-minute mark, and Bradley will hope that they continue their ruthlessness on Thursday.
Had Ferencvaros played at the weekend, Cherchesov may have been prepared to make numerous changes to his side given the size of their lead.
However, he could now show preference to retaining the same XI, wanting to give his first team at least an hour of competitive football before a return to domestic action on Sunday.
Franck Boli is pushing for a return down the middle of the attack and could potentially get the nod over Ryan Mmaee.
Shamrock Rovers possible starting lineup:
Mannus; Hoare, Cleary, Grace; Finn, O'Neill, Towell, Lyons; Watts; Greene, Gaffney
Ferencvaros possible starting lineup:
Dibusz; Wingo, Botka, Knoester, Paszka; Besic, Laidouni; Auzqui, Nguen, Traore; Boli
We say: Shamrock Rovers 1-3 Ferencvaros (Ferencvaros to win 7-1 on aggregate)
With pride at stake, we expect Shamrock to do everything possible to push their more illustrious opponents on Thursday evening. However, we cannot see anything but an away win, potentially with the game having remained on level terms come the half-time whistle.