The Europeans had plenty of ball and almost grabbed an equaliser through Ivan Saponjic in the 76th minute, but his driving shot was saved by goalkeeper Gaston Guruceaga.
Just a few moments later, Sergej Milinkovic barely blasted wide of the goal, but there would be one more golden opportunity for the Serbs to salvage a point.
Saponjic made a run on goal in the 83rd minute to create a one-on-one chance with the goalkeeper, but again Guruceaga was up to the challenge.
The Uruguayans would have felt hard done by had he scored, as Saponjic appeared to be well offside when he made his run.
Serbia pressed right until the end of stoppage-time, but could not find the back of the net.
However, despite the loss, Serbia can take plenty from a match it probably deserved to draw.