"I thought the ref had a poor first half, but as poor as he was in the first half he was as good in the second," said Warnock.
"But I think my half-time team-talk did the trick really - I asked him if he wanted some smelling salts.
"I didn't think the concentration level was good enough from him in the first half.
"We were punished with the first goal."
Warnock added: "I can't say enough good things about my side - an absolutely incredible little bunch.
"We deserve to be in the hat and it will not be an easy game for them down at Selhurst Park."
Claude Davis was stretchered off midway through the first half after an innocuous aerial challenge with Sam Vokes.
He received around five minutes of attention from as many as 10 medical staff before heading to hospital.
But Warnock played down any concerns over a serious injury.
"We should know later today, he's had a scan locally and they couldn't see anything wrong with his neck," he said.
"But the consultant wants to look at him first before they let him out.
"We're hoping he'll be all right."
"I thought we had some chances to win it in the second half and Crystal Palace played well.
"We didn't get anything other than what I expected from them.
"What I got from us, though, at the start of the first and second half is not what I expect.
"We've had to have a scrap, it was a cup tie.
"We've had to work harder than necessary just to get a draw."
He added: "Of course our best chance has gone but we drew away at Everton, we beat Spurs away and we drew at Stoke.
"We want to be in the FA Cup, and we are."