Karadzic criticised Antic's tactics in Serbia's 2-1 defeat by Australia which resulted in a group stage exit and said the failure to reach the knockout rounds had cost the FSS an estimated $5 million.
"Our ambition was to reach the quarter-finals, while the failure to do so will be a huge financial blow and it means we will have to cut costs on all levels," Karadzic told the FSS website.
"That includes coach Radomir Antic, whose team selection against Australia, when we played with only one striker and we needed to win, will also come under scrutiny.
"It doesn't mean we will part company but he will have to accept a pay cut because his improved contract was based on the assumption that we would achieve more in the World Cup and earn an additional $5 million."
Antic's contract with the FSS expires after Euro 2012 and Karadzic made it clear that qualifying for the event was a top priority for the 61-year old coach.
"Reaching the European Championship is the only way to heal our World Cup wounds," he said.
"Our campaign in South Africa was not a complete disaster because we beat triple world champions Germany, but we have to be ruthlessly honest to ourselves and say that we have failed to live up to expectations."
Serbia finished bottom of Group D with one win and two defeats, having lost their opening match to Ghana 1-0 before beating the Germans by the same score.
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