It was the second successive unimpressive performance by the Serbians, who lost 1-0 to New Zealand on Saturday and again looked bereft of ideas.
Their reshuffled line-up struggled in midfield and the strikers wasted the few good chances carved out on a rain-sodden pitch.
Antic rested defensive mainstay Nemanja Vidic and the back four looked all at sea in the opening 30 minutes, only two superb saves by reserve goalkeeper Bojan Isailovic keeping the teams on level terms.
Lacking guile, pace and creativity, the Serbians had to rely on counter-attacking and came close with two breaks shortly before half time through fit-again Danko Lazovic and strike partner Nikola Zigic.
Four substitutions at the interval upped the tempo of Serbia's game as substitute Dragan Mrdja found space on the right flank and Zoran Tosic was lively on the left.
One of Mrdja's darting runs presented Marko Pantelic with a simple chance but the long-haired striker blazed his shot from three metres over the bar with Poland's goalkeeper Lukasz Fabianski beaten.
Serbia play their final warm-up against Cameroon in Belgrade on Saturday before flying out to Johannesburg.
They open their Group D campaign against Ghana in Pretoria on June 13 before playing Germany and Australia.
