"There'll be plenty of criticism of this decision. We understand and accept that," Annesley said.
"The people involved are polarising in some ways and the issues involved are polarising as well.
"The board had to weigh up all of the information and the board are the only ones with all of the information."
Hayne is contracted until the end of the 2018 season and his own future at the club remains unclear.
Annesley would only say Hayne was contracted and "like all of our contracted players we expect them to perform their contractual obligations" when asked if the fullback would remain at the Titans.
The search for a new coach will begin immediately, Annesley said, with current Queensland State of Origin mentor Kevin Walters among those speculated as contenders.