Cheika believes Jones went over the top in his attempts to give England a psychological edge during their tour of Australia in June, when the tourists recorded a 3-0 series win.
Jones, who guided Australia to the 2003 World Cup final, accused the Australian media of being disrespectful, but Cheika believes his former Randwick team-mates needs to have a look at his own behaviour.
"There was a lot of vitriol about Australia, his home nation," Cheika told reporters at a press conference in London ahead of Saturday's clash between England and Australia at Twickenham.
"It's where he coached, where the opportunities were given to him to grow up as a coach and play.
"Personally, if you're looking to leave a legacy somewhere, you don't want to hit back at it when you leave."
Jones has already taken a pre-match swipe at Australia by calling for a meeting with referee Jaco Peyper so he can raise concerns about the Wallabies' scrummaging.
Cheika laughed off Jones's remarks following Australia's 27-24 loss to Ireland in Dublin at the weekend, but he believes the former Japan coach has taken his mind games too far.
"I'm not 100 percent sure what's gone on after Saturday, but I'm sure he'll be into it," said the former Leinster coach.
"In June I sort of gave the opportunity to see how a former Australian would deal with it. It's a bit like the goal-scorer who scores against his old team, you know?
"I suppose it's always difficult when you go back into a tournament where you're playing teams you've coached before. And you don't really know how to play it.
"Do you stay reserved or do you go out there and get stuck into them? I know what I do, even in a country like Ireland when I'm there, where I coached for many years.
"I didn't coach the national team there, but that's the choice he wants to make and he thinks is best for his team."
Cheika voiced an intention to arrange a meeting with referees' chief Alain Rolland over his side's heavy penalty count against Ireland, but admitted he had yet to receive a reply from the Irishman.
"That's probably a little bit where Australia's at at the moment," said Cheika.
"We don't have a lot of referees on the panel. We've only got one on the panel. We don't have any high-rollers at World Rugby level, so we have very little say at the moment in those areas.
"And we've got to improve, that's part of our thing. We've got to get more referees up there and involved at that level, because of the top-tier nations, we have the least representation at the referees' table."
Original source: Jones has tarnished his legacy in Australia - Cheika