The hosts started the half brightly and had territorial advantage as well as better ball possession, with Charlie Adam in the thick of things.
Craig Levein's side had a good chance to break the deadlock in the 23rd minute when Robert Snodgrass forced a save from Serbia goalkeeper Vladimir Stojkovic.
The visitors were put into trouble again a minute later when Steven Naismith failed to find a proper touch with his head to a fine delivery.
However, Serbia soon came into their own in the game and started to create chances, as the pace of the match became relentless.
The final chance of the first half fell to Serbia on the stroke of half-time when Darko Lazovic forced Scotland goalkeeper Allan McGregor with a shot from 18 yards.