"We feel we have been prejudiced right from the outset," the Premier League club said in a statement expressing disappointment at the timing of the FA's announcement on Monday.
"The FA introduced a new policy to handle our application on the back of consultations with the City Till We Die group, and we therefore feel that our application was already pre-judged," it added.
"This feeling has been reinforced with yesterday's announcement, as the club feels this will further prejudice the forthcoming ballot of season pass holders."
Hull City's Egyptian-born owner Assem Allam, who bought the club in 2010, wants to change the name for next season because he believes Hull Tigers would help generate more revenue.
He has said he will walk away from the club, who face third tier Sheffield United in the FA Cup semi-finals next month, if the request was turned down.
The proposed name change has provoked fierce opposition from fans campaigning under the banner 'City Till We Die' to keep the 109-year-old name.
The FA said on Monday that its Membership Committee had made a unanimous recommendation, when it met last Wednesday, to reject Hull City's request.
The recommendation will now be discussed and voted upon at a full FA Council meeting on April 9.
Hull said it was now "time for the silent majority to come forward and support the club's aspirations". The club said details of a ballot would be sent to season ticket holders in the next 48 hours.
- Sports & Recreation
- Hull City