The flashpoint happened towards the end of the first half when Davis caught Cardiff defender Roger Johnson in the throat with a flying arm.
A shaken Johnson needed medical attention but clearly felt he could continue and remonstrated with Jones on the sidelines, but his manager decided otherwise.
Jones, who had already seen Michael Chopra hobble off, was clearly seething at seeing Davis go unpunished and had an angry exchange with the on-loan Derby player at half-time on the way to the tunnel.
Jones was held back by security guards as tempers boiled over, with players and coaching staff from both sides getting involved in the fracas.
"I was not happy with what happened to one of my players," admitted Jones after the game.
"Go and get the video and see it for yourself.
"I didn't need the video to see what happened. Roger was left spitting blood and he's been sent to hospital.
"It would take a lot to force Roger off. He tried to go back on but he did not know what was happening.
"We have to go and see him in hospital. Roger was distressed at half-time and for him to go off, there must have been something wrong.
"If he went back onto the pitch, he would have looked around and got hold of the person who did it and throttled them."
The incident brought an end to entertaining opening half in which Cardiff took the lead through Scotland international Ross McCormack.
McCormack converted a 20th-minute penalty after Nathanial Clyne tripped Joe Ledley in the area.
It was no less that Cardiff deserved as Chopra had put the ball in the net in only the third minutes only to see his effort chalked off for offside.
Jay Bothroyd also went close on a couple of occasions while Palace's best chances of the half fell to Shefki Kuqi and Victor Moses who were both denied by full-stretch saves from Stuart Taylor.
Neither manager emerged for the second half, during which Palace were denied two penalty appeals.
First Rui Fonte went down in the area under a challenge from Gabor Gyepes.
Referee Booth then turned down appeals for what looked a clear handball by Mark Kennedy in the 64th minute.
Palace's youngsters battled to defy their age and press for a leveller and as the thunderous tackles continued, so too did the flurry of yellow cards.
But Cardiff punished Palace's cavalier attitude when McCormack raced through the Eagles' defence to slot home his second of the match in stoppage time.
Palace boss Warnock was at a loss to understand why he was sent to the stands and demonstrated how he felt Johnson had collided with Davis' arm.
Warnock said: "I don't really know why I was sent off. The referee said it was to calm things down and make both of us go up there.
"Your reputation goes ahead of you sometimes. But Dave was misinformed. Claude didn't elbow him. If anything, he ran into his arm.
"I don't think Claude will get done for that. There was no arm movement at all.
"Both teams wanted to win, and we didn't throw in the towel. But I like Cardiff. I hope they go up."