The Turkish midfielder, who was heavily linked with Chelsea last month, will miss the rest of the season after FIFA opted to impose the initial ban which has now been upheld.
Trabzonspor took the matter to the Court of Arbitration for Sport (CAS), who have ruled in favour of them, despite it having nothing to do with Leverkusen.
"We regret this decision which we cannot comprehend," said Leverkusen sports director Rudi Voeller.
"Leverkusen is not involved in the dispute with Calhanoglu having joined in 2014 from Hamburger SV.
"This is a big blow both for Hakan and for us. Although Bayer Leverkusen had nothing to do with this it is also punished.
"Now we will miss an important player during a key part of the season."