The Uruguayan was working as an analyst on the BBC's Match of the Day live coverage of the Confederations Cup match between Spain and Nigeria.
During the first-half of that game, Brighton released a statement on their website saying: "Gus Poyet has been informed today by Brighton & Hove Albion Football Club's internal disciplinary panel that his employment has been terminated with immediate effect."
However, Poyet only learned about the sacking when a member of the BBC production staff handed him a print out of the statement.
He is now set to launch an appeal against his dismissal, which he believes is the "right thing to do" after the decision from the club.
"You've got yourself a great story," Poyet told BBC presenter Mark Chapman when asked about the issue.
"I've still had no communication from the club, no text, no email. The only thing I'm concentrating on is the appeal. I will appeal because it's the right thing to do.
"I'm probably the first to be in this position. Everyone can make their own conclusions about the way I have been informed by you.
"I suppose reading the statement I will be able to talk to them. It's very sad, they made me proud. Not being able to answer a phone or text is unusual.
"Are they messing with my career? We will see, it's too early to say. I am looking forward to clearing this."
Former Chelsea midfielder Poyet, 45, was initially suspended and now has the opportunity to appeal the decision to sack him despite the club saying they are looking for an interim manager for pre-season.
Brighton's statement continued: "Poyet's sacking followed his suspension, an investigation, and a subsequent formal disciplinary process. In line with the club's own procedures, and UK employment law, Mr Poyet now has a right of appeal. As such, the club will make no further comment on this matter or recent LMA statements at this time.
"Given the close proximity of the new season, the club will, in conjunction with its board, now seek to appoint an interim manager pending the outcome of a possible appeal. The interim manager will oversee the initial weeks of pre-season preparation alongside the club's existing staff.
"The club's first-team players report back as planned for pre-season testing tomorrow, Monday 24th June, with the squad's first technical sessions commencing on Thursday 27th June. The team play Whitehawk on Saturday 6th July and leave for their summer training camp in Spain on 14th July."
The 45-year-old, assistant manager Mauricio Taricco and coach Charlie Oatway were subsequently told to stay away from the club in the wake of a disciplinary hearing, although Taricco's ban has since been lifted.