The side's achievement in qualifying for Euro 2013 was overshadowed by scenes of chaos and violence immediately after the final whistle in Krusevac.
Connor Wickham's injury-time strike, which clinched a 2-0 aggregate success, prompted a hail of missiles from the crowd and scuffles broke out moments later.
Serbian supporters, players and other officials appeared to get involved while Danny Rose was sent off after the final whistle for reacting angrily to apparent racial abuse.
A statement from the FA read: "The FA condemns both the scenes of racism and the confrontation at the final whistle during which time our players and staff were under extreme provocation.
"The FA has reported a number of incidents of racism to UEFA following the fixture.
"These were seemingly aimed at a number of England black players by the crowd. The matter is now with UEFA."
Watch: England vs Serbia U21 turns ugly... More Videos
Rose was pushed in the back as he left the field and gestured that monkey taunts had been aimed towards him. England assistant coach Steve Wigley was also caught up in the trouble and was manhandled as he made his way to the tunnel.
Head coach Stuart Pearce told BBC Sport: "One or two of the technical staff from the opposition, and I don't include their manager in that, didn't cover themselves in glory on the pitch at the end.
"Punches, headbutts were thrown, and God knows what else. We will let the authorities deal with this at UEFA."
Pearce had spoken before the game of his confidence that the issue of racism would not raise itself.
A match between the two countries at the 2007 Under-21 European Championship in Holland was marred when England defender Nedum Onuoha was racially abused.
Serbia were fined £16,000 by European governing body UEFA after that incident, but Pearce had said he thought the game in the Balkan country had moved on since then.
Former England captain Paul Ince, working as a pundit on ESPN, believes tougher action is necessary this time.
Ince, whose son Thomas had been playing in the match, said: "It is disgraceful. There is no excuse for the scenes we have just seen.
"There were punches being thrown; if it was me they would be kicked out for the next five tournaments, European, World Cups."
The under-21 side's captain Jordan Henderson was also proud of the reaction of his team-mates under the circumstances.
Henderson told TheFA.com: "The players coped with the abuse really well. It's not nice. They kept their heads and were professional.
"The players completely condemn what happened. There were also stones, coins and seats getting thrown at us."
In terms of the action, England produced another fine display of defensive resilience, recording a sixth clean sheet in seven outings to protect their 1-0 first-leg lead and reach next summer's finals in Israel.
Wickham wrapped up victory by rolling the ball into an empty goal to finish off an injury-time counter-attack which had seen the Serbian goalkeeper go forward for a set-piece.