"This is where the umpires need to step in as soon as they start to hear stuff," former Australia opener Katich told ESPNcricinfo, having called the match.
"Give the warnings to the skippers and get the skippers to control it.
"That obviously hasn't happened, and now it is tit for tat with the teams blaming each other for who started it.
"It's a shame because what happened on the field obviously lit the fuse for then what has happened off the field. It has overshadowed what was a fantastic test."
Former South Africa spinner Paul Harris agreed on both counts, saying "the umpires might need to have a bit more of a say".
Du Plessis expressed similar sentiments to Katich in his post-match press conference.
Ravi and Dharmasena delivered few lectures in the first test, with the exception of rebuking Kagiso Rabada for his send-off of Warner on day three. Katich noted it was important Crowe now "nips this in the bud".
"If it is allowed to keep going on, then things are going to get out of control as we saw in the tunnel," he said.
"I look back on my time and I think things might have been pretty tame compared to this stuff."
The second test that starts in Port Elizabeth on Friday.
Ravi will be on third-umpire duty when South Africa attempt to level the series, with Dharmasena in control alongside Chris Gaffaney.
AAP