The Eagles lost out to the Swans at Selhurst Park as Angel Rangel notched a late winner for the Welsh side to move them off the bottom of the table, and leave Sam Allardyce's men just a point and a place above the relegation zone.
Delaney, who captained the side in the absence of injured skipper Scott Dann, says they must quickly put things right in training.
"We're way below where we should be, but we can't make excuses. We can't dress it up," he told the club website.
"They've been playing reasonably well and they showed the concentration that maybe they've lacked. But having said that, to get back to 1-1 and to lose to a late goal is crazy."
He added: "There's no point blaming other people, it's on our shoulders now. We've got to get back to the training ground, get back to work."