Football's world governing body announced on Wednesday it had banned the Spanish champions from the transfer market for two consecutive windows and fined them 450,000 Swiss francs (£305,000).
The Spanish football federation (RFEF) was fined 500,000 Swiss francs (£340,000) after FIFA found it had also breached rules on the transfer of minors.
Barca denied wrongdoing and said they would move to get the transfer ban suspended until their appeal is heard and would take the case to the Court of Arbitration for Sport (CAS) if necessary.
Bartomeu fiercely defended the Catalan club's La Masia academy, which has produced the likes of Lionel Messi, Xavi and Andres Iniesta, at a news conference on Thursday.
He said Barca would push ahead with plans to buy at least a goalkeeper and a central defender in the close season.
"We are outraged and the victims of a grave injustice," Bartomeu told reporters.
"With this sanction, FIFA is punishing a model that has existed for 35 years and which is the essence of this club.
"FIFA knows that we do things well and we look after the children and give them an education that perhaps they wouldn't get in their own country.
"We are not prepared in any way to give up our educational model. We have defended, continue to defend and will always defend the rights of minors.
"Hands off La Masia, that's the message we want to send to our members and fans, hands off La Masia.
"We will fight until the end to protect this model because it has made our first team become a leader in world football.
"We have absolute confidence in our lawyers and they tell us we have good grounds to think that the sanction will be lifted."
FIFA's punishment was the latest blow to the club and came after Bartomeu's predecessor, Sandro Rosell, was forced to step down in January amid allegations of misappropriation of funds and tax fraud linked to the signing of Brazil forward Neymar.
Rosell has always denied any wrongdoing.
Argentina forward Messi and his father have also been implicated in a tax fraud probe and Bartomeu suggested there may be a concerted campaign to damage the club.
He said it was "very strange" that the FIFA decision to sanction Barca, which he noted came after an "anonymous denunciation", had been taken at the end of November but not communicated to the club until more than four months later.
"We have noticed for quite a while now that someone is trying to damage Barca and we are investigating," he said.
"We have suffered many things these past years and we are suffering this now.
"We have a certain amount of evidence which makes us think that someone wants to damage Barca and we will fight it.
"When we have the evidence we will not stop and we will go after those who are behind this.
"We are starting to accumulate solid evidence. Barca has been leading world football for a long time and things are done well here.
"This is the greatest club in the world and perhaps there is someone who doesn't like that and wants to damage the club.
"They won't succeed because we will all fight it and it will all come out in the end."
Bartomeu was repeatedly asked who would want to damage the club, including if it might be arch rivals Real Madrid, but he declined to provide any names.
Barca have 18 football players from outside Spain currently training at La Masia including seven from Cameroon, three from Guinea-Bissau, two from Morocco, two from South Korea and one each from Nigeria, Senegal, France and Germany, Bartomeu said.
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