Uefa announced the charges against the Turkish club for the feline invasion during the club’s last-16 encounter with Bayern Munich at their Vodafone Park home.
Play had to be stopped by English referee Michael Oliver until the animal vacated the pitch, with the German giants winning 3-1 on the night.
The fine of £29,841 was for insufficient organisation, as well as the throwing of objects and blocked stairways.
In comparison, the RFU were fined £22,000 from Fifa for fans’ racist chanting in a March friendly against France.
Bayern themselves were charged £21,942 for a pitch invasion and illicit banner in the first leg of their semi-final defeat to Real Madrid on April 25, while Roma were fined £6,143 for the setting-off and throwing of fireworks and warned over time-wasting by ball boys in the second leg of their last-16 clash with Shakhtar Donetsk on March 13.