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
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 their 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.
Ex-Lazio and Fiorentina man Mihajlovic seems to be building for the future, fielding a side that had an average age of just 23.
Craig Levein, meanwhile, opted to not include any Old Firm players in his side, with only Celtic's James Forrest representing either of the Glasgow giants on the bench.
After a frenetic start, McGregor had to have his wits about him 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 defence 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 team-mate Miller crying out for it in the middle.
The away side's defensive shape was non-existent, and after pouncing on a hurried ball out from the back Charlie Adam released Miller with an inch-perfect first-time ball but the Cardiff striker's cross-cum-shot landed on the roof of Stojkovic's net.
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, 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 Dusan Tadic for Lazovic on the hour.
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.
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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.
Snodgrass, who had faded dramatically since his impressive first-half cameo, was taken off with 20 minutes to go as Levein brought on the exciting James Forrest to try and show more of a threat going forward.
It was the Serbs, though, that began to show more attacking intent, as the home side ominously invited them into their half, with the defensive line becoming deeper and deeper from a Hampden Park faithful perspective.
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.