Poyet had an appeal for unfair dismissal rejected this afternoon, thus officially ending his four-year association with the South Coast side.
He told The Independent: "I was very disappointed to get the sack and even more the way they did it. I think I deserved more respect.
"For the achievements we had together, the fans, players and staff, as a manager I deserved a better outcome, like a meeting with the people from the club and not to have it done when I was on TV. I didn't expect to finish this way after what we did together, the fans, the players and the staff.
"Sometimes when you leave a club you hold a press conference. It is important the fans know that I appreciate the way they treated me and supported me, from the first game with 7,000 there to my last game at the Amex with 32,000 people. It was spectacular. They were very patient with me."
Poyet infamously learned of his dismissal by Brighton officials live on television, while working as a BBC pundit during the Confederations Cup last month.