Warner was hit with three demerit points for the offence and also fined 75% of his match fee, about A$13,500, after meetings between the match referee Jeff Crowe and Australian team management on Tuesday night and Wednesday morning.
De Kock on Wednesday unsuccessfully contested his level-one charge of bringing the game into disrepute, resulting from a derogatory comment.
While he is now on notice, needing only one more demerit point against his name in the next two years to be banned for a Test, Warner declared he would not change the way he carried himself on the field.
Crowe ruled the original punishment of one demerit point and a fine should stand.
Although held back by four different teammates during his verbal attack on De Kock, Warner said he did not intend to get physical with him.
CCTV footage from the tunnel at Kingsmead showed Australia vice-captain Warner and De Kock involved in a fiery discussion as players climbed the stairwell to their dressing rooms during the tea break on day four.
New footage shows the pair walking from the ground together and Warner is heard to call De Kock a "f****** sook", according to The Australian newspaper, referring to someone who is soft or easily upset.
Did Quinton de Kock say something about Warner's wife? .
AUSSIE coach Darren Lehmann expects the coaches and captains of both teams to "chat" before the second Test against South Africa starts in Port Elizabeth on Friday after a bad-tempered start to the series. They are saying they didn't cross the line but where is the line, who sets the line, where did the line come from?
David Warner and family arrive in Port Elizabeth.
"The match officials and the ICC they govern the game, and the umpires on the field must take charge of the game". When they hear things, they must take charge and don't leave it to: oh, we didn't cross the line.
Reverse swing was a feature when South Africa beat Australia by 231 runs in 2013/14.
I'm telling them to focus on cricket but if I keep poking at you all the time, I'm sure you will respond as well.
Off-spinner Nathan Lyon was fined 15 per cent of his match fee for breaching the ICC's Code of Conduct as he dropped the ball onto a sprawled AB de Villiers after the batsman had been run out in South Africa's second innings.