England won the match on October 16 1-0 after scoring with the last kick of the game, and fighting broke out between players and officials immediately following the final whistle.
"Having reviewed the television footage of the incidents, the FSS disciplinary committee decided to ban Ninkovic and Mudrinski from playing for Serbia at any level for a period of one year," the Balkan country's governing body (FSS) said.
"Also, staff members Srdjan Maksimovic and Andreja Milutinovic have been banned from their coaching duties at any level for Serbia for two years. All four have violated the FSS ethics and fair-play code."
England Under-21 left back Danny Rose has complained he was racially abused by Serbia fans before, during and after the game.
The FSS have denied the racism charges, which will be decided upon by UEFA when the European governing body's disciplinary committee convenes on Nov. 22.
UEFA President Michel Platini said on Tuesday Serbia could face tough sanctions if television footage proved home fans made monkey chants at Rose.
"Over a year ago we gave Croatia and Serbia a serious yellow card, now we will see what the disciplinary committee will decide," Platini told reporters at a Euro 2016 meeting in Paris.
"We will get the report from the delegates and the report from the officials, we have the television footage - the disciplinary committee will deal with it."
The FSS said after the game in the central Serbian city of Krusevac that Rose had provoked the home fans in an "inappropriate, unsportsmanlike and vulgar manner" after England scored to win 2-0 on aggregate and advance to next year's finals in Israel.
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