The home side had an early chance to get on the scoresheet as Mehmet Topal delivered a low drive towards the net after receiving the ball on the edge of the box, but the goalkeeper managed to get a slight touch to bounce the ball off the post.
Some aggressive tackles were administered in the early stages of the game, with three yellow cards being issued before the 15th minute.
Nadir Ciftci tried to make things happen for Celtic as he unleashed a shot in the box, but the ball was blocked by Fenerbahce's defence, which resulted in a corner that came to nothing for the Scottish side.
The visitors tried to ramp up the pace of the game, but their attacking plays lacked an end product, with one particular movement resulting in Ciftci failing to control the ball, which allowed Fenerbahce to snatch possession.
After a sniff at goal, Fenerbahce increased pressure on the visitors and it eventually paid off when Markovic, who is on loan at Fenerbahce from Liverpool, netted from close range.
Ironically, Gordon, who had been on top form prior to this move, made a blunder, which allowed Markovic to sneak in.
Celtic are already out of the Europa League, while Fenerbahce are in second place.