FFK president Fadil Vokkri said that Friday's decision contrasted with Monday's ruling by European soccer's governing body UEFA to admit the British colony of Gibraltar as a provisional member.
FIFA had agreed in principle to allow Kosovo to play friendlies last May but, following opposition from Serbia and UEFA president Michel Platini, has dallied over how to implement the ruling.
FIFA says it will now discuss the matter at its next executive committee meeting in Tokyo in December.
"We are extremely disappointed with the postponement by the FIFA executive committee of the decision on the modalities of the decision taken by the same body last May, authorising FIFA member associations to play friendly matches with teams and clubs from Kosovo," said Vokkri in a statement sent to Reuters on Tuesday.
"We do not understand the reasons behind this, in particular when one sees the double standard shown by UEFA between the situation of Kosovo, recognised by 91 countries in the world.....and the situation of Gibraltar, a non-independent territory recognised by no one with embryonic football.
"We are surprised by this difference of treatment in light of the obstruction we have been facing for years now."
"Maybe the method adopted by the Gibraltar FA - going to the Court of Arbitration for Sport (CAS) - should have been adopted by us.
"We chose a realistic approach with sensible solutions based on football facts and we have not been heard."
Kosovo declared independence from Serbia in 2008 but has not yet won recognition from the United Nations (UN) itself, although many UN members countries do recognise it.
FIFA and UEFA policy is that only nations recognised by the UN can be accepted as members.
The FFK has made it clear that it is not seeking membership, but simply the right to play non-competitive matches.
UEFA said on Monday that it had agreed to admit Gibraltar provisionally following a ruling by CAS.
Gibraltar, which has a population of 27,000, has been trying to join UEFA for over 10 years but its application has faced fierce opposition from Spain.