Sunderland followed up a 1-0 Tyne-Wear derby success over arch rivals Newcastle United with a dismal showing at the Stadium of Light on Saturday.
Glenn Murray's opener and an 11-minute hat-trick from Yannick Bolasie blew Sunderland out of the water and left them just three points above the drop zone with six games remaining.
"If we carry on performing like this then we have no chance," Advocaat said. "[Am I] worried? Yes. Very worried. I'm as worried as the other coaches who are in the same position as ourselves.
"We are not the first team to get beaten by Palace, because they have beaten better teams in the last nine games. But we have to believe in ourselves. We showed we can do something against Newcastle.
"I see for myself that we don't create enough chances even though we play with three strikers.
"It is not about looking at other results, we have to do it by ourselves."
