The Tartan Army served up a largely profligate performance, with Steven Naismith the main culprit as they drew a blank in their opening 2014 World Cup qualification match
The Serbs, who had won just one of their last 10 matches, were worth their point but Craig Levein will be sure to reflect on a largely wasteful afternoon in front of goal for his side.
Steven Naismith was the main culprit as he missed a golden chance to secure all three points when he was put clean through, but his indecision cost him dearly as his effort sailed wide of Vladimir Stojkovic's post.
Serbia created numerous chances, as its technical superiority often told, but found Allan McGregor in top form as he served up fantastic stops to deny Aleksandar Kolarov, Danko Lazovic and Dusko Tadic.
In what was a frantic opening at Hampden Park, both sides looked to kick-start their qualifying campaigns and it was the hosts who carved out the first meaningful opening of the match.
New Everton signing Naismith escaped down the Serbia left but when he shifted the ball onto his right foot, as he sought to narrow the angle, his low effort was blocked.
Just minutes later, the Scots could have been behind. McGregor had to have his wits about him early on to deal with Kolarov's low free-kick. The Besiktas keeper produced a superb stop low down to keep out the Manchester City wing back's bending strike around the wall.
Robert Snodgrass was proving a constant thorn to the Serbian defense and after a free-kick was taken quickly, following a foul on the Norwich winger, he escaped his man with ease but could not quite apply the finishing touch with teammate Miller crying out for it in the middle.
Manchester City's new signing Matija Nastasic was enduring a torrid time at center half, looking nervy in a very suspect Serbian backline and received the first booking of the game for a reckless tackle on the onrushing Alan Hutton, with the Aston Villa man looking set to escape down the right flank.
The Scots' tempo had increased throughout the match but the Serbs offered a timely reminder that they were still part of the contest as a powerful strike from Lazovic from the edge of the area forced McGregor into a low stop.
After a fairly insipid opening to the second half, Aleksandar Ignjovski tried an ambitious shot from the edge of the area, with a powerful, swerving effort as he looked to make the breakthrough and secure what could be a crucial win for his nation on the road.
The pace of the game began to slow, with both sides looking tentative but Mihajlovic sought more creative impetus up front and reacted by throwing on Tadic for Lazovic on the hour mark.
Miller's superb movement caused Serbia trouble from a few corners with Morrison's lofted passes finding the veteran striker, but he was unable to turn in the best opportunity he mustered for himself with Stojkovic blocking his dinked shot.
Then, within a matter of minutes, the two best chances for both sides came, and sadly, went.
Kolarov was the first to come close to breaking the deadlock, as he gathered a fizzed ball into his path and rifled in a low strike which flew just inches beyond McGregor's far post.
But it would be the hosts who would miss an absolute sitter to seize the lead they craved on the break.
Naismith was the beneficiary of some superb play from the excellent Caldwell, but after being released by the Wigan stalwart, he clipped harmlessly wide of the post with just the keeper to beat in what would be the best Scottish chance all afternoon.
There was still time for both sides to try and find that elusive opening, and surely winning, strike but when McGregor dealt with Tadic's low effort well and Stojkovic denied a hurried low shot from substitute Forrest, the time was up for both.
For both sides, it can be seen as a hard-fought point, but after Levein insisted that his side was capable of winning every game in the group, it may well be the Scots that will go home the more frustrated with this result.