Despite playing for the whole of the second half in ten men, Birkirkara went close to earning a draw against Diósgyőr but the Hungarians ended winning 2-1 at the Debrecen Stadion in Debrecen, Hungary.
However a 1-2 defeat away from home still leaves good chances for Birkirkara to qualify for the next round.
Birkirkara coach Paul Zammit opted to start with new signings Edmond Agius and Rafael Ledesma on the bench, only naming Spanish goalkeeper Adrian Murcia Sanchez in the starting line-up. Agius and Rafael were included as substitutes.
David Barczi put Diósgyór ahead on 34 minutes but the Stripes were quick to equalise thanks to a direct freekick by Matheus Bissi da Silva.
Matheus Bissi da Silva picked a second yellow card one in the second half, therefore leaving the Stripes in ten men.
The game seemed heading for a draw but three minutes in added time, Patrik Bacsa notched the winner for Diósgyőr.
The second leg will be played at the National Stadium on Thursday.
DIOSGYOR Ivan Radoš, Senad Husić (67′ Lazar Marjanovič), Tamas Kádár, William Alves, Drazen Okuka, Andras Gosztonyi (56′ Gabor Bori), Mark Nikházi, Akos Elek, David Barczi, Patrik Bacsa, Miroslav Grumić
B’KARA Adrian Murcia, Matheus Bissi, Nikola Vukanac, Alejandro Mendoza Corujo, Gareth Sciberras (74′ Edmond Agius), Paul Fenech, Ryan Camenzuli (60′ Ryan Scicluna), Joseph Zerafa, Zach Muscat, Edward Herrera, Terence Vella (82′ Rafael Ledesma).