Home captain Michael Clarke was fined for using an obscenity while warning James Anderson to expect a broken arm.
Former Australia wicketkeeper Ian Healy said: “Umpires are fairly insipid and don’t take on their responsibilities anywhere near enough.
“Maybe it’s time they stiffen up their act.”
Healy, who played 119 Tests for Australia between 1988 and 1999, feels that umpires must take more of an active role in calming potential spats.
He told Cricket Australia: “I like an aggressive spirit but if it gets too personal and too violent in its intentions it needs to be looked at.
“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.
“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.”
Former Australia spinner Shane Warne has claimed that Clarke was responding to comments made by Anderson towards George Bailey towards the end of the opening Test, which Australia won by 381 runs.
Neutral umpires are used for Test matches but only four of the 12-man elite panel are not Australian or English – Aleem Dar and Kumar Dharmasena, who stood in the first Test, Marias Erasmus and Tony Hill.
To help ease the strain on that quartet, New Zealand’s Billy Bowden, who was dropped from the Elite Panel of umpires in June, has been brought back for the Ashes series.
Next week’s second Test in Adelaide will see Dharmasena and Erasmus officiate together, while Erasmus and Bowden will take charge of the third Test in Perth.
The fourth Test will feature Dar and Dharmasena, while Erasmus is on the field for the final Test in Sydney with Dar.
Hill will be used in three of the remaining four Tests as the television umpire – Erasmus did the first Test and Bowden will do the fourth.
England return to action on Friday when they take on Chairman’s XI in a two-day game in Alice Springs before the second Test starts on 5 December.