Healy believes umpires have become too hesitant to step in and nip potentially ugly incidents in the bud, as fallout from Clarke and James Anderson's first Test stoush continues.
Despite allegations Anderson instigated the incident by threatening to punch Australian short-leg fielder George Bailey, Clarke has been the only player fined from the match, after his reply was inadvertently broadcast via the stump microphone.
The incident is believed to have been just one of many heated exchanges throughout the match, and Healy insists umpires Aleem Dar and Kumar Dharmasena could have done more to prevent the situation spilling over.
"I like an aggressive spirit but if it gets too personal and too violent in its intentions it needs to be looked at," he said. "The line in the sand that we talked about is in the preamble for the laws of cricket. That's how you play cricket.
"It's all written and it's all there and if umpires are of the opinion that it's not really being adhered to then they've got to step in.
"But I think umpires are fairly insipid and don't take on their responsibilities anywhere near enough these days. Maybe it's time they stiffen up their act."
The former Test wicketkeeper was concerned that Clarke had been singled out over the incident.
"Hopefully the umpire's report was accurate and consistent with everything else that went on in the game," he said. "The umpires heard it all. If it was happening both ways from both sides then I hope that (Clarke's) one was over the top compared to everything else that happened in the game."