Defender Danny Rose was sent off after the final whistle after apparently responding angrily to monkey taunts from the crowd at the end of the Euro 2013 play-off in Krusevac.
Scuffles also broke out when supporters invaded the field moments after Connor Wickham struck in injury time to complete a 1-0 win on the night and 2-0 aggregate success.
FA statement: "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."
Steve Wigley, a member of England's backroom staff, was also caught up in the trouble as players left the field at the Mladost Stadium.
Head coach Stuart Pearce told ESPN: "I think there were one or two racist incidents that came on from the crowd and they have been reported to UEFA, I believe, by ourselves.
"It is in their hands now, they will have to deal with that.
"I am very proud of my players and my staff and very proud of the achievement in getting to a fourth tournament in a row.
"It is very sad, but we are united as a team and a staff.
"A lot is happening in our country with regard to stamping out racism and I am very proud of the reaction of our players towards the end.
"It is a real shame because over two ties it was a really close game - two good teams going hammer and tongs at each other.
"It is just a shame it was soured in the last few minutes of the second leg of the tie.
"Savo Milosevic, their technical director, has come to our dressing room and apologised for any behaviour that was unsavoury.
"I never want to see any football matches end like that, this is a sporting arena.
"The important thing, when the dust settles, is we are going to a championships because we deserved to over two legs.
"Our players have put a lot of hard effort and sweat to get there. There is a real collectiveness here. We will let the authorities deal with this.
"All we know is we have given a good account of ourselves over two matches, we have won nine out of 10 matches in qualification and I am very proud of my team."
Former England captain Paul Ince: "If you are black, it is hard to actually keep control of yourself because you are the one having the racist chants.
"From looking at what we have seen on TV, they have done very well to keep cool heads.
"It is a shame because tomorrow we will be talking about something we don't want to talk about. What we should be talking about is England qualifying for Israel in 2013."
The ugly scenes at the end overshadowed what had been another superb defensive performance by England.
SERBIA 0 ENGLAND 1
ENGLAND: 1. Jack Butland 2. Adam Smith 6. Craig Dawson 5. Steven Caulker 3. Danny Rose 7. Wilfried Zaha 76' 4. Jason Lowe 8. Jordan Henderson 10. Tom Ince 9. Marvin Sordell 62' 11. Nathan Delfouneso 89'
Subs: 13. Ben Amos 12. Ryan Bennett 14. Tom Lees 62' 15. Josh McEachran 16. Raheem Sterling 76' 17. Andros Townsend 18. Connor Wickham 89'
England Under-21s claimed their place at Euro 2013 amid unsavoury scenes during their qualifying play-off in Serbia.
Players appeared to be pelted with missiles after Connor Wickham struck in injury time of the second leg to book England's trip to next summer's finals in Israel.
Supporters came onto the field, scuffles broke out and England's Danny Rose was sent off after the final whistle. He reacted angrily by kicking away the ball and appeared to indicate he had been racially abused as he left the pitch.
Steve Wigley, one of the England coaching staff, also appeared to become caught up in the trouble as the players left the field.
The ugly scenes overshadowed another fine display of defensive resilience from England.
Stuart Pearce's men recorded a sixth clean sheet in seven outings to hold out the Serbs on a wet and windy night at the Mladost Stadium in Krusevac.
Marvin Sordell hit the post early on but, until Wickham came off the bench to stroke into an empty net late on, the game was largely about England's defensive effort.
Serbia had shown from the outset they intended to be more positive than they were in Norwich last week and, with Nikola Ninkovic coming into the side, they had a much greater cutting edge.
But it was England who had the first serious opportunity as Sordell hit the woodwork after nine minutes.
Captain Jordan Henderson found the Bolton forward with a superb through-ball but Sordell cracked his shot against the near post after neatly cutting inside Slobodan Medojevic to create space 12 yards out.
Serbia goalkeeper Branimir Aleksic looked uncertain throughout but escaped punishment after spilling a Henderson corner and was then fortunate to earn a free-kick as Craig Dawson jumped to reach a Wilfried Zaha free-kick.
The hosts showed their danger as Nemanja Kojic found space down the right and pulled the ball back for the livewire Ninkovic, who shot tamely at Jack Butland.
Luka Milivojevic flashed a volley wide after a Nemanja Gudelj throw-in was only partly cleared by Steven Caulker.
Serbia went closer as Henderson's headed clearance from Darko Lazovic's free-kick found its way to Ninkovic at the far post but his shot went across goal and wide.
Aleksic had another lucky escape as Dawson beat him to a Rose free-kick on the edge of the area but the England defender could not keep his header on target.
Lazovic found room on the edge of the England box but his attempt to curl a shot into the top corner was easily dealt with by Butland.
After a brief hold-up when one of several flares lit by Serbian fans found its way into Aleksic's goal area, the hosts continued to press as Ninkovic beat Adam Smith but fired wide from distance.
Further efforts came in from Kojic and Milivojevic as Serbia ended the first half on top but Butland was not tested.
England had a scare early in the second period as Kojic broke clear but Smith got back well to cut him off and was harshly booked for his trouble.
Ninkovic went close again after the ball fell to him outside the area but his swirling effort was well pushed put by Butland.
Ninkovic turned provider as he picked out Filip Malbasic with a fine ball but England were relieved to see the substitute flagged offside after Ognjen Mudrinski took a needless touch.
Thomas Ince broke clear as England mounted a rare attack but Zaha stumbled as he latched onto his cross and was bemused to be booked for diving.
Aleksic went forward as Serbia had a late chance from a free-kick but England broke away through Ince, who slid in Wickham, prompting the mayhem that followed.