The Uruguayan was suspended by officials in May after the team's Championship playoff semi-final defeat to Crystal Palace.
Poyet then refused to attend a disciplinary hearing for legal reasons and was sacked for gross misconduct.
The former Chelsea and Tottenham Hotspur midfielder appealed the decision citing unfair dismissal, but Brighton informed him last month that he had failed with his challenge.
"I know the allegations," Poyet told Sky Sports News. "I hope we go to court. It's the best way for the truth to come out."
Oscar Garcia was appointed Brighton's new manager on June 26.