The sanction, imposed by UEFA's independent control and disciplinary panel on Thursday following disturning scenes in their play-off match against England Under-21s, has been widely criticised for being too lenient, with the fine equating to just under £65,000.
UEFA itself can appeal to increase the severity of the punishment. UEFA sources said the organisation's president Platini has taken note of the sanction and will make a final decision once he has read the full file on his return from Japan next week.
The European body's prosecuting inspector had proposed more "drastic" measures, the Serbian federation has admitted.
QPR defender Anton Ferdinand, the target of racial abuse by John Terry last year, contrasted the sanction against Serbia with the 100,000 euro and one-match ban handed to former Arsenal striker Nicklas Bendtner for displaying a betting firm's logo on his underpants during Euro 2012.
Ferdinand tweeted: "Wow UEFA ain't serious with their punishment... So showin a sponsor is worst than racism and fighting!"
His brother Rio added: "Uefa are not serious at all on racism. Fines do not work at all. They have zero impact on federations/clubs/fans/players £fact.
"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 £simple."
The Football Association also criticised the sanction and will appeal against two-match and one-match bans for Steven Caulker and Tom Ince respectively.
FA general secretary Alex Horne said: "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."
The FA 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 subjected to monkey chants throughout the match and as he left the pitch.
Serbian FA secretary general Zoran Lakovic appeared to suggest that the UEFA official prosecuting the charges had also demanded tougher action.
Lakovic said in a statement: "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 Kick It Out, slammed the sanction as "a paltry slap on the wrist", adding: "Again we haven't seen decisive action from UEFA."
Piara Powar, executive director of European anti-discrimination body FARE, said UEFA had failed to display the necessary leadership.
Powar said: "The original offences warranted a more severe collective punishment than a ban on spectators for one match.
"This is a moment in which leadership to challenge discrimination is needed from all authorities. This sanction falls short of that objective."
Serbia and the FA have three days in which to lodge an appeal - while UEFA themselves can also appeal against the control and disciplinary body if they too think the independent commission has been too lenient.
Lord Herman Ouseley, chairman of Kick It Out, has called for matches to be stopped if there is racist chanting from the crowd.
Ouseley, who has described the punishment as "paltry", has demanded more drastic action, telling BBC Radio Four: "If necessary games should be stopped and sections of the crowd who are behaving badly should be shown the door."
The Football Association expressed its disappointment at the punishment for Serbia, but Ouseley attacked the FA for undermining his organisation's efforts with their treatment of the John Terry and Luis Suarez cases.
Asked if football was slipping back into the bad old days, Ouseley added: "It clearly is if you have your position undermined by people who are in powerful positions, and I am talking about the FA."
Peter Herbert, chairman of the Society of Black Lawyers, described UEFA's stance on racism as "abundantly weak".
"As far as Serbia is concerned, (UEFA) doesn't even include the word racism or discrimination in their final report," he told Sky Sports News.
"What did they think was going on then? Did they think people were having a tea party?
"It just beggars belief as far as we're concerned that they should take such an incident, which is not the first time the Serbian FA have been guilty of this in terms of the conduct of their fans, and actually after the second or third occasion give what is effectively a green light to this happening again."