Wallabies coach Cheika said England's "niggle" off the ball went beyond mere physicality, and said his players needed to cope with it better after the 39-28 defeat at Lang Park.
"If someone pulls you down, you can't whack a bloke because you know you're going to get caught," Cheika said this week.
"So, I'm not doing niggle. That's not our go. We've got to play more physically ... If that's your strategy then that's your strategy, good on them."
Australian Jones rejected Cheika's assessment and said the match at Lang Park was played in a fair spirit.
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“We’re a physical team," a stone-faced Jones told reporters in Melbourne on Thursday.
"We’re not concerned about Australia. If they want to say things about us -- we’ve been respectful about them, the way they play the game and conduct themselves on the pitch.
"To me the first test was a fantastic game of rugby.
"If the series continues in that spirit I think it’s going to be one of the great rugby series. So Michael’s got his opinion and good luck to him."
Past Wallabies players and media pundits also lined up to question England's scrum after the loss at Lang Park, with former Australia coach Bob Dwyer accusing England prop Dan Cole of illegal tactics and referee Romain Poite of failing to crack down on them.
Dwyer made similar accusations against England prop Joe Marler before Australia's World Cup clash with the hosts last year.
Marler was subsequently penalised repeatedly for scrum infringements by the same referee in that match as England were sent spinning out of the tournament.
South African referee Craig Joubert will officiate in the second test at the Melbourne Rectangular Stadium on Saturday and his scrum interpretations could prove decisive.
Jones said Joubert was unlikely to be influenced by Dwyer or any other aggrieved Australian pundits.
"We’ve played under Joubert against Wales and we thought he was a very good referee," Jones said, before revealing that he had given World Cup-winning coach Dwyer a call earlier in the day.
"I’ll quote someone, Bob Dwyer always says -- I actually spoke to him this afternoon -- he always says you can fix a team in one week," Jones said.
"And you can. You can fix problems in one week.
"I won’t tell you the rest of (the conversation),” the cagey Australian added with a grin.
(Editing by Toby Chopra)
