Matt Phillips' 85th-minute goal made it an unhappy return to his former club for Holloway, whose current side are now six points behind Hull in second place.
"We need to show character and keep fighting," said Holloway. "I thought the overall performance showed we were calm and still believed in ourselves.
"We didn't panic and kept going. That really should have been a 0-0. We're not making things happen for ourselves. It is really important at this time of the season that we all stick together.
"It's the worst run we've had since the start of the season and it's the wrong time to do it. We've just got to dust ourselves off, get up and get on with it.
"It's no good feeling sorry for ourselves and we need someone to step up to the plate."
Holloway refused to blame the poor surface at Bloomfield Road for the defeat after Glenn Murray and Wilfried Zaha missed the best of the few chances Palace created.
"The pitch is no excuse as its no help for both teams, but it doesn't help. Unfortunately we didn't make the most of our advantage as we didn't really create that much. I think that's the most difficult thing."