Both UEFA president Michel Platini and Serbian FA President Tomislav Karadzic are unhappy with the decision, announced by FIFA on Tuesday as neither supports the idea.
Platini said he was unhappy that FIFA made the decision with "president Blatter not speaking to anyone first."
"It's a political decision, it is not a football decision," he said.
Blatter addressed UEFA's delegates on Wednesday at their confederation meeting ahead of the FIFA Congress on Thursday and Friday to explain FIFA's stance.
In an interview with Reuters on Tuesday he said the move was a positive one to help football in Kosovo develop and that he hoped it would accelerate their desire to become a full member of UEFA and FIFA in due course.
Karadzic said in a statement on the Serbian FA website: "Granting Kosovo full accession to UEFA and FIFA is out of the question because that decision would clearly contravene UEFA's statutes, which stipulate that one can join UEFA only if recognised as an independent country by the United Nations."
The statement continued: "President Karadzic explained to UEFA and FIFA officials that an array of negative and harmful consequences would hit the region and Europe in general if the decision was allowed to stand, while he also strongly protested about it being made behind closed doors, without the presence of the Serbian Football Association."
On Monday the Football Federation of Kosovo (FFK) welcomed the move, while in a statement on Wednesday FIFA said Serbia and UEFA were invited to a meeting in Zurich on May 31.
But FIFA also said: "We would like to stress that the FIFA Executive Committee made clear that such authorisation does not constitute a step towards FIFA membership, which depends on other considerations.
"In particular, and according to both the current and draft statutes of FIFA, as long as FFK is not a member of UEFA it cannot be a member of FIFA. The decision was intended purely to support the development of our sport."
The outcome of next week's meeting will be submitted to the extraordinary meeting of the FIFA Executive Committee which is planned for July 4.