But they showed their quality in dispensing of Wolves 3-0 in the previous round of the FA Cup while league results had also been healthy until the mid-week setback against Swansea.
O'Neill said: "I saw Palace play Wolves and they deserved to win the game and played very strongly that night - and it helps when you get a six minute hat-trick!
"There is a good spirit amongst them and that would come from the manager. I can't say we know each other really well but I have a great appreciation of him.
"He has done very well in his career, is a terrific motivator and, every club he has been at, the players want to play for him.
"He engenders a great spirit wherever he goes and that is a hallmark of someone who knows what the managerial game is all about.
"People say he has a habit of getting under people's skin. That is true, that is also part of his make-up.
"Like a lot of us, he doesn't adhere himself to everyone and that is the nature of this business.
"Personally speaking, it probably doesn't matter a jot to him - and quite rightly so."
O'Neill added: "I think there has been a galvanising effect at Palace from players and supporters (since going into administration) and the game will be very tough in front of close to a full house.
"They were right in the promotion race and that deduction of points can be debilitating and knock your whole season. As it turns out, they've got plenty to play for again.
"Palace are fighting for their lives. It's a great opportunity for them, a great opportunity to keep the club going and they'll be looking forward to it. It's a game that's very much in balance."
O'Neill is saddened to see Palace's current predicament and is aware of the potential the club possesses from his days as a player.
He said: "There seems to be almost a (financial) case per season and there has been now for about 20 years. Somebody always seems to find themselves in trouble. This is nothing new.
"But, where it is particularly galling, is for clubs the size of Crystal Palace.
"Palace have a fantastic catchment area and I've played in that ground when they were in the big league - the old First Division.
"There's 40,000 people been at Selhurst Park, so they've got the wherewithal to be a really big club.
"That Croydon area is a football hotbed and I've thought that for a long time.
"They are a 'proper' club so it's rather disconcerting that a club of that size should find themselves in that sort of trouble."
Villa have an extra incentive to make the quarter-finals at the first attempt as any replay would have to take place in the week leading up to the Carling Cup final against Manchester United at Wembley on February 28.
O'Neill said: "In an ideal world it would be great to have a free week ahead of the final, a full eight days to prepare after playing Burnley next weekend.
"But we are not in the choice business. The Palace game will be very difficult and, if the tie goes to a replay, you just have to get on with it."
Villa captain Stiliyan Petrov and 12-goal leading scorer Gabriel Agbonlahor are major fitness worries ahead of Sunday's game.
Petrov and Agbonlahor suffered ankle and leg injuries respectively during the mid-week home draw with Manchester United and regarded as "doubtful" by Villa boss Martin O'Neill.
O'Neill has indicated he will again make changes for the competition and the likes of Brad Guzan, Nathan Delfouneso, Steve Sidwell, Curtis Davies and Habib Beye could come into the equation to start.
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