Salzburg started Thursday night’s contest at Parkhead with intent, with Jonathan Soriano and Christoph Leitgeb fizzing dangerous crosses into the Celtic box during the game’s opening stages.
And Salzburg did not have to wait long for the opener when Massimo Bruno’s shot on eight minutes deflected off Charlie Mulgrew into the path of Alan to volley past Craig Gordon.
Celtic almost hit back instantly when Gordon’s clearance fell into the path of Leigh Griffiths who fired over, but back came Salzburg with Martin Hinteregger going close to doubling their lead.
And they got the second goal their play deserved in the 13th minute when Andre Ramalho flicked a header from a corner across goal for Alan to prod home from close range.
But after Soriano had a shot from an indirect free-kick disallowed, Celtic managed to pull a goal back on the half-hour mark. Emilio Izaguirre burst clear down the left before crossing for Stefan Johansen to volley low and hard past Peter Gulacsi in the Salzburg goal.
Johansen almost got Celtic back on level terms four minutes before the interval after some neat interplay with Griffiths but his shot was blocked by Hinteregger.
Celtic weathered the early Salzburg pressure after the restart and won a flurry of corners without seriously troubling Gulacsi as the game drifted past the hour mark.
But Salzburg continued to threaten with Soriano firing wide after a clever one-two with Ramalho, before the Spaniard flashed a ball across goal which eluded Alan’s lunge.
Celtic had a glorious chance to equalise after another fantastic cross from Izaguirre was met by Griffiths’ header at the back post, but Gulacsi scrambled across his line to save superbly.
But there was still a sting in the tail for the home side in added-time. A fast break from Marcel Sabitzer saw him drill a shot at Gordon which he saved but the ball dropped to Naby Keita who looped his header over the keeper.
Despite the defeat Celtic will travel to Dinamo Zagreb for their final match in Group D safe in the knowledge that their place in the Europa League knockout stages has been secured.