Smith labelled Warner "a fool" while also saying that Lyon might regret his huge celebration following AB de Villiers' run out at Kingsmead.
"We've got used to Davey over the years. I think he'll probably say it was unnecessary himself", Smith said.
"As an outside observer, I think you would find that a little bit off-putting at times, a little bit bad taste at times", Gilchrist told a radio station.
The remaining home hopes evaporated when du Plessis was clean bowled by Cummins, adding just four runs, and leaving South Africa reeling at 49-4.
And with that big step came even bigger celebrations, with David Warner sending some words of wisdom Aiden Markram's way and Nathan Lyon dropping the ball suspiciously close to the prostrate de Villiers.
The incident occurred while the players were going up the steps for the tea break on the fourth day of the first Test in Durban.
It took Australia 18 minutes and 22 balls to claim the last South African wicket when De Kock swung across the line and was leg before wicket to Josh Hazlewood for 83.
It seems to have happened in heat of the moment from Lyon, who would have been ecstatic with the Australians felling De Villiers for a duck, but the off-spinner seemed to have forgotten that each move of the cricketers is scrutinized carefully, and any deviation from the "spirit of the game" is met with frowned eyebrows.
Lyon contacted de Villiers on Sunday night to apologise, telling the veteran there was no malice intended.
Sharing his thoughts on that incident, Graeme Smith said: "The Aussies were pretty fired up at that time pushing for a victory. I think it needs to be considered how to react in certain scenarios and learn from them", Gilchrist emphasised.
The video shows Warner being restrained by Australia batsman Usman Khawaja and spin bowler Nathan Lyon as he directs a verbal barrage at De Kock, who left the field as South Africa's not-out batsman at the same time as the Australians. They won the game by 118 runs and have taken a lead of 1-0 in the series. AB de Villiers then returned to the pavilion after facing just one ball and without troubling the scorers.