The former Chelsea midfielder was dismissed by the Seagulls at the weekend, with the Uruguayan seemingly learning his fate while appearing on Match of the Day.
Poyet suggested that he had not received any communication from the club about his impending dismissal, but a statement from Brighton has quelled such claims.
"In relation to comments made by Gus Poyet on Match of the Day last night, the club would like to point out that its disciplinary panel considered the matter on the afternoon of Friday, June 21 and for most of Saturday, June 22," read the statement.
"The club spent much of Sunday, June 23 in discussion with Gus and his representatives. For legal reasons we cannot say anything about the content of those discussions but Gus was well aware, before he appeared on the BBC last evening, that his dismissal was pending.
"Given Gus has a right to appeal the decision to dismiss him, the club will not be making any further comment on this matter at this time."
Poyet was suspended by Brighton last month.