The Seagulls were due to host Millwall over the festive period, but the game has now been moved eight days earlier due to transport and safety concerns.
"It's absolutely embarrassing, with every single person in this country convinced that Boxing Day is the most important date in football. Somehow we are not able to play and it shows it depends who it suits," Poyet told Brighton newspaper, The Argus.
"If it suits the fans, everyone would say we should play, if it doesn't suit the bus drivers or trains or whatever it is, we cannot play.
"So, at the end of the day, from my point of view, it's once more people picking and choosing what is good for themselves and not what is good for football or the country, for history. It's very individual, really, really selfish, I would say.
"From 1997, when I came to England, people say you have to play on Boxing Day."