Poyet was appearing on BBC's Match of the Day programme as a pundit when Brighton released a statement confirming his dismissal.
The 45-year-old, who had been suspended by the club since last month and was the subject of a disciplinary hearing last week, said during half-time of Uruguay's clash with Spain: "I think the BBC have a great story forever, because a manager getting information that he is being released from his employment by the BBC is quite surprising.
"I have had no communication, no texts, no email."
In response Brighton have released yet another statement as the feud between the two parties rumbles on.
"In relation to comments made by Gus Poyet on BBC 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."
With Poyet set to appeal, the Championship club are searching for an interim manager.
Reports in Spain claim former Barcelona midfielder Oscar Garcia, who left his position as boss of Maccabi Tel Aviv last month, is in line to eventually take over.