Goals from Ferdi Kadioglu, Jack Hinshelwood and Danny Welbeck gave the hosts a comfortable win that sent them above Chelsea into sixth, leaving the Blues seven points behind fifth-placed Liverpool with just four games remaining.
Co-owner Behdad Eghbali was in the stands to watch the capitulation unfold.
Rosenior said, "That was unacceptable in every aspect of the game. I'm hurting and I feel numb. The attitude was unacceptable. I keep coming out and defending the players but that performance tonight is indefensible.
"The manner of the goals we conceded, the amount of duels that we lost, the lack of intensity in the team — something needs to change drastically here right now.
"I can't keep coming out here and defending some of the things that we are seeing. The general attitude, spirit and determination was lacking, apart from maybe three or four of the 11. That is nowhere near enough for this club.
"The performance in terms of professionalism wasn't there. It was a really, really difficult night — the most difficult night so far at this magnificent football club but also in my career because some of the things I was witnessing today I never want to see again."
Rosenior was asked whether he still commands the faith of his dressing room after Moïses Caicedo was seen jogging back as Brighton scored their second.
"It's not about playing for me. It's about playing for the club, for the shirt. That performance in itself was damning. It stood against what I believe in."
Furious Chelsea fans directed chants at Rosenior throughout the second half, with sections of the away end telling him to leave. He offered what appeared to be an apology to supporters at full time.
"I understand the fans' frustration. The buck stops with me."
The head coach has Sunday's FA Cup semi-final against Leeds at Wembley to attempt to stop the rot.
"I will pick a team that will represent the club in the correct manner," he said.