Hoops returning midfielder Callum McGregor, only starting due to a midfield crisis, gave the home side the lead and some hope in the third minute with a drive.
The Dutch side recovered and by the time Arkadiusz Milik levelled in the 21st minute they were bossing most of a wide open match but Celtic reasserted themselves only to be stung in the 88th minute with Cerny’s breakaway winner to win 2-1, although Fenerbahce’s win against already-qualified Molde made the result academic.
Celtic remain bottom of Group A with two points with their final match against Fenernbahce in Istanbul next month a dead rubber.
The Hoops had got off to a dream start when McGregor took a pass from Craig Mackay-Steven and edged inside on to his right foot before despatching a shot from 20 yards past Ajax keeper Jasper Cillesen.
The visitors were clearly rattled but they slowly composed themselves.
Fischer took advantage of a deflected strike from Lasse Schone which landed in his path inside the box and although Celtic keeper Craig Gordon beat away his close-range strike, he headed the rebound back across goal where Polish striker Milik knocked it over the line.
The promise of goals at either end remained in the second half, although both defences had tightened up.
But with five minutes remaining, after Cillesen had made a comfortable save from Griffiths, the impressive Younes crashed a shot against Gordon’s post before Ajax broke and Cerny, on for Fischer, drove in number two to sink the home side.
Gordon,Lustig,Boyata,Simunovic,Tierney (Izaguirre 78), Forrest,Armstrong,Rogic (Mulgrew 66),McGregor, Mackay-Steven (Allan 71),Griffiths.
Cillessen,Tete,van der Hoorn (Sanogo 80),Riedewald,Dijks, Schone (van de Beek 72),Klaassen,Gudelj,Fischer (Cerny 68), Milik,Younes.
Felix Zwayer (Germany).