Fast bowler Johnson was the match-winner for the hosts as England were trounced by 381 runs in a controversial series opener at the Gabba.
The match was overshadowed, to an extent, by angry on-pitch confrontations between James Anderson and Michael Clarke - and the Australia captain was subsequently fined almost £2,000 by the International Cricket Council.
David Richardson, ICC chief executive, has since confirmed both Clarke and his opposite number Alastair Cook will be spoken to by match referee Jeff Crowe - in an attempt to calm the atmosphere - before the second match of five in Adelaide next week.
England coach Andy Flower also appears amenable to speaking in a similar vein to his Australia counterpart Darren Lehmann.
The tourists were especially unimpressed by Australia opener David Warner's public remarks about Jonathan Trott's "poor" and "weak" batsmanship in Brisbane.
Trott was twice dismissed cheaply by Johnson, and has since flown home with a stress-related illness.
After taking nine wickets in the match, however, Johnson is determined to stick with Australia's recipe for success.
"I think it's worked for us. I definitely think they're rattled by it," he said.
"They don't like it at all.
"Obviously their coach has come out and wanted a truce from what I've heard.
"That's not going to change from our end."
Richardson, meanwhile, has confirmed to the Daily Mirror that Crowe intends to address both captains on the issue of 'sledging'.
"The match referee will be speaking to the players from both teams, but no charges have been laid other than the one brought against Clarke," he said.
"I don't want to comment on specific incidents and specific players, but I think generally our attitude towards abusive language is that it is immature and unnecessary and not supported.
"What we want to do is make sure it does not get out of hand with disrespectful, disparaging comments or abusive comments - and the match referee will be talking to both teams before the second Test.
"Our attitude is to let the action speak rather than words. That is more effective - hard, aggressive cricket yes, but let's not stoop to abusive or disparaging comments."
- Sports & Recreation
- Alastair Cook