Palace saw their hopes of gaining an automatic promotion spot stutter as they failed to see off a Seasiders side that were battling with 10 men for 48 minutes.
Defeat made it three straight losses for Palace, who are now six points behind Hull in the final automatic promotion place and the Tigers have a game in hand.
On his return to Bloomfield Road, Holloway saw both Glenn Murray and Wilfried Zaha miss chances but believes now is not the time to start pointing fingers.
"It took a strike like that from the edge of the box that's got them all three points," he said.
"We need to show character and keep fighting. 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.
"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.
"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."
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- Wilfried Zaha