Poyet was suspended as Seagulls boss after their play-off semi-final defeat to Crystal Palace before being sacked for gross misconduct in June.
Brighton chairman Tony Bloom claimed Poyet, who joined the club in 2009, informed him in March that he wanted to leave the club at the end of last season.
The Uruguayan led Brighton to the League One title in 2011 and then to the club's highest league finish for more than 30 years in 2013.
Poyet said: "There are several reasons but unfortunately this will probably go to court. Because I totally disagree with every allegation and accusation the club has put on me.
"I will take action because I think it's important for me. I'm quite confident
and relaxed but I hope we will go to court because it is the best way for the
truth to come out.
Oscar Garcia replaced Poyet as head coach but got off to a disappointing start with a 2-1 defeat at Leeds on the opening day of the championship season.
"I would like the club to focus on Oscar because he deserves the support of everyone. You get disappointed with being sacked but I can live with it," added Poyet.
"But I think I deserve better respect and the way they sacked me when I was on tv was disrespectful and unfair."