"Not then go sledging and stay off the field and say: 'Oh sweet boys go to it.' That's why I don't want to do that because you've got to go back it up."
Jones' calculated media performances have included tirades against the "demeaning" treatment his side is getting in Australia; citing several promotional clips on FoxSports in particular.
Chris Robshaw even told English media he used the ribbing in the advertisements as motivation.
But Cheika said his side would not follow suit, saying he wanted his team to be "bulletproof" to external criticism.
"I think that's only short-term motivation always," Cheika said.
"For us we've obviously there'd be things said about us from the sidelines or whatever but we want to build some substance to be a consistent team for the long haul.
"Not just get by beating them this week and hope for the next thing "That's not what we're about and I want to be bulletproof to all that stuff and build from within.
"Not have to use that thing to stick on the wall or that thing to stick on the wall to help us."
Cheika said he had not read the latest comments from Bob Dwyer attacking the legality of England's scrummaging.
They prompted aggrieved England prop Joe Marler - who is not on tour but copped a similar Dwyer critique last year - to tweet: "Bob Dwyer is a w***nker".
"I haven't seen them. What did he say?" Cheika said.
"I'm thinking about my team. It's not my position to assess the opposition.
"Internally, yes, and especially after they've towelled us up the week before in the game. We're just humble, work hard, get ourselves ready and get ready to reload this weekend. The last thing I'm looking at is worrying about if this guy did this or that guy did that from the opposition."
Cheika said he was not concerned about his team's physicality, as Jones suggested, but was more concerned about getting stronger in the face on off-the-ball "niggle" from England.
The Wallabies were upset after the Brisbane game that players were being held back at rucks and five-eighth Bernard Foley getting tackled late several times.
"There was a lot of niggle off the ball. That's not physicality, that's something else," Cheika said.
"Niggle's the stuff you do off the ball so you're protected. You can't do something - if someone pulls you down, you can't whack a bloke because you know you're going to get caught."
Asked what ways they could react to niggle, Cheika said: "We'd have our idea but I don't think this is the place to be able to talk about."