The control and disciplinary body also banned six players for varying terms, including English duo Tom Ince and Steven Caulker, and two Serbian coaches after ugly scenes marred the end of the European Championship play-off.
The FA had reported the racist abuse to UEFA plus a number of other incidents. Full-back Danny Rose, who was dismissed after the final whistle for kicking the ball away in anger, complained he had been particularly targeted.
Rose claimed he was subjected to monkey chants throughout the match and as he left the pitch.
General secretary Alex Horne said afterwards that the FA would have to consider whether England should play in Serbia in the future.
Caulker has been given a two-match ban and Ince a one-game suspension but a charge against the FA of failing to control their players was dismissed by UEFA.
The Serbia FA has also been fined 80,000 euros (£65,000) "for the improper conduct of its supporters during and at the end of the match, as well as for the improper conduct of the Serbia players at the end of the game".
Serbia fitness coach Andreja Milunovic, who attacked England officials, has been banned for two years, the second of which is suspended for three years. Serbia assistant coach Predrag Katic was also banned for two years, the final six months of which suspended for three years.
Four Serbia players were also banned - Goran Causic for four matches, Ognjen Mudrinski and Filip Malbasic for three and Nikola Ninkovic for two.
Serbian FA secretary general Zoran Lakovic admitted the sanctions were "a final warning".
He said in a statement: "Though this case followed a very large media campaign, I do not think the members of the UEFA control and disciplinary commission were influenced by that.
"If we take into account what the drastic proposed penalty by the disciplinary inspector Jean-Samuel Leube we have not been hit so hard.
"I believe that this is a final warning to all of us who work in Serbian football, including coaches and players and fans, because for even the smallest mistake UEFA can now impose the most rigorous punishment."
Lord Herman Ouseley, chairman of football's anti-discrimination group Kick It Out, slammed the sanction for Serbia as "paltry".
He said: "Kick It Out shares the concerns of many in football that abuse aimed at black players isn't taken seriously enough. This is a paltry slap on the wrist and again we haven't seen decisive action from UEFA."
Sports minister Hugh Robertson, who had written to UEFA president Michel Platini demanding tough action for the racist abuse, expressed his disappointment.
Robertson said: "I am disappointed in the punishment that has been awarded to the Serbian FA given the widespread racist abuse that England's Under-21 team suffered that night. Racism is completely unacceptable and we need tough sanctions to help combat it."