Thomas Ince and Steven Caulker have been banned over incidents that took place during
England Under-21s' win over Serbia
Four Serbian players have also been banned, while two of their coaches are suspended for two years.
Uefa has ordered Serbia to play their next competitive under-21 match behind closed doors, and they have also been fined £65,000.
FA general secretary
“The scenes were deplorable and we do not believe the sanction sends a strong enough message.”
The FA is set to appeal against Ince and Caulker's one and two match bans.
England's players were racially abused during the 1-0 victory in Krusevac.
Uefa will send the FA its full written reasons for its decision and the FA then have three days to decide whether to appeal.
But FA general secretary Alex Horne said: "It is The FA's vehement belief that its players and staff acted correctly in the face of provocation, including racist abuse and missiles being thrown.
"We are therefore surprised to see that two of our players have been given suspensions.
"We shall await Uefa's reasoning but it is our intention, at this stage, to support our players and appeal these decisions.
"We are disappointed with the sanctions levied by Uefa with regards to the racist behaviour displayed towards England's players.
"Let's be clear, racism is unacceptable in any form, and should play no part in football. The scenes were deplorable and we do not believe the sanction sends a strong enough message."
Horne also confirmed that the FA is unable to formally appeal for Serbia to be given a harsher punishment.
England head coach Stuart Pearce insists his players did nothing wrong.
He said: "I am concerned to see our players suspended by Uefa and we will continue to support them.
Racist chanting sparks scuffles
"I maintain that our players played no part in the aggression. From what I witnessed our players and staff were forced to protect themselves in the violent scenes that followed the game."
Uefa said Serbia were punished due to 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".
Blackpool winger Ince, 20, will sit out the England Under-21s' Euro 2013 game against Italy in June, while Tottenham defender Caulker, 20, will also be absent from the match against Norway.
Uefa's control and disciplinary body dismissed disciplinary proceedings opened against the Football Association.
Serbia assistant coach Predrag Katic has been banned from football for two years, with the final six months suspended for a probationary period of three years.
Fitness coach Andreja Milunovic has been banned from all football-related activities for two years, with the second suspended for a probationary period of three years.
Recent Uefa fines
to Porto for their fans' racist abuse during the Europa League match against Manchester City.
to Lazio following racist chanting during a Europa League game against Tottenham.
to Manchester City for being one minute late back onto the pitch after half-time against Porto.
to Denmark striker Nicklas Bendtner for revealing a sponsor's logo on his underpants during Euro 2012.
Ognjen Mudrinski and Nikola Ninkovic have already been suspended for a year
by the Serbian Football Federation and they were handed respective three and two-match bans.
Goran Causic has been suspended for four games and Filip Malbasic is banned for three matches.
Minister for Sport Hugh Robertson said: "I am disappointed in the punishment that has been handed 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."
Manchester United defender Rio Ferdinand
"Uefa are not serious at all on racism. Fines do not work at all. They have zero impact on federations, clubs ,fans (and) players.
"Uefa need to talk to this generation. They don't seem to be up to date on this issue. Harsh punishments needed as a deterrent."
Kick It Out's Troy Townsend, whose son Andros played in the game in Krusevac, thinks that the penalties against the Serbian federation were not heavy enough.
He told BBC Radio 5 live Drive: "Steps need to be taken to make sure these things don't happen again and I'm not sure that is going to be the case.
"It's not nice for anyone to be watching those pictures, players being chased around the pitch, the chanting and England management being hit.
"I feel that Serbia have got away with it and the [Serbian] FA needs to be accountable.
"It's great fining them and banning the players, but at some stage the FA have to be held accountable and it's not the first time they've been involved in incidents and they're getting away with it again with a slap on the wrist."