Fabian Hurzeler’s side qualified for European football with an eighth-placed finish last season but have lost Danny Welbeck and Jan Paul van Hecke over the summer.
And they looked short of ideas in attack in a tricky, tense and tight first leg.
Hurzeler fielded new signing central defender Luka Vuskovic in an otherwise fairly familiar if far from first-choice XI which looked like there is work to do before the end of the transfer window.
Welbeck scored 14 times last season and his goals, and experience, will be hard to replace, while midfielder Carlos Baleba was left out as he is linked with a move to Manchester United.
The Seagulls were dominant in possession but found it tough to break down an organised opposition. Georginio Rutter went close in the first half, before Bart Verbruggen had to make an excellent sprawling save to deny Heine Åsen Larsen.
Substitute Charalampos Kostoulas headed on to the roof of the net late on but there was to be no breakthrough.
Brighton host Tromso in the second leg next week with the winners advancing to the league phase of the Conference League.
Brighton reached the last 16 of the Europa League in 2023-24 before being knocked out by Roma.
They start their Premier League campaign against Aston Villa on Sunday.
