The 45-year-old, who insists he has not been contacted by the Championship club, was informed of the decision while working as a pundit for the BBC
The announcement of Poyet's sacking was announced while the 45-year-old was working as a pundit for the BBC's coverage of the Confederations Cup.
The Championship club confirmed the decision was made following their internal disciplinary procedure. Poyet had failed to appear at Brighton's hearing earlier in June.
"I think the viewers and everyone can take their own conclusion about the way I've been informed by you [the BBC]," Poyet said.
"The only thing I'm concentrating on is the appeal. I will appeal. I think it is the right thing to do. I cannot say any more because after this I will talk longer with my lawyers. It is difficult to make any comments.
"I need to read everything first but I will appeal because whatever they [Brighton] said in the email I know myself, and I know I want to make everything is clear."