It is believed that the Reds were insulted by the offer from Alkmaar after 18-year old Birighitti completed a 10-day trial with the club.
"They have made an offer which wasn't adequate for the player Mark is," Reds football director Michael Valkanis said.
"You don't really find an under-21 keeper capable of being a senior No.1. We could look all over the league but we won't find an under-21 keeper as good as Mark. He's the future of Australian football.
"They are trying to take him away on the cheap from us and, at some stage, the A-League clubs have to make a stand. We deserve more respect."
The club expects Birighitti to remain at the club until at least January when his current contract runs out.
"We don't stand in the way of players going but it has to be the right deal," Valkanis added.
"Mark is young. He is the best going around at his age. He will go over but we will help him to when the time is right. We did that with Nathan Burns and Bruce Djite and won't hold Mark back either."