The punishment was imposed by FIFA's disciplinary committee on Tuesday after a group of supporters racially abused Denmark substitute Patrick Mtiliga every time he touched the ball in October's Group B qualifier in Sofia.
In an unusually strongly-worded statement, FIFA described the incidents at the Vasil Levski stadium as "offensive, denigratory and discriminatory".
"Our main motive will be that we were punished disproportionately for racism and discriminatory behaviour of a very small group of the crowd in the Bulgaria v Denmark match," BFU's president Borislav Mihaylov said in a statement.
"[We were punished] not only with a game behind closed doors but we were also fined 35,000 Swiss francs.
"In fact, we are sanctioned twice for the same thing, which is not fair," added Mihaylov, who is also an executive committee member of European football's governing body UEFA.
The BFU said it will seek the support of the interior ministry to try to identify the trouble-makers and impose stadium bans "for a long time".
The ban came as FIFA's European counterpart UEFA is accused of being too lenient on cases of racism, letting offending clubs off with fines.
Bulgarian media described the punishment as "deserved" and "logical", blaming local authorities for doing too little to deal with the problem.
