Jones' seven-year England reign ended in December despite a record as England's most successful boss, with a win rate of 73%.
But Rugby Football Union chiefs felt compelled to act after a poor run of results culminating with a 2022 in which England won just five of their 12 matches, and Jones was replaced by Steve Borthwick (43).
When asked on Wednesday whether he had any regrets over his exit, Jones replied: "No, none at all.
"I had a great seven years here, I loved it. I bet I'm the last foreign coach who coaches for seven years here. First and last.
"Loved my time here and I'm looking forward to Sunday. The sun is shining. It will be unbelievable."
England were booed off the field following Jones's final game in charge, a 27-13 defeat by South Africa at Twickenham, but Jones had no concerns about the reception that awaits him this weekend.
"I never worry about things I can't control," said the Australian. "I don't control that, so it's no use even thinking about it."
Jones took over after England's woeful first-round exit on home soil at the 2015 World Cup and took the team all the way to the 2019 final in Japan, where they were beaten by South Africa.
But even though his contract ran until this year's World Cup in France, the RFU decided to ditch Jones, also a former coach of Japan.
Australia are currently a lowly seventh in the global rankings but Jones said they could still come good at the World Cup.
"We've got plenty of talent," said Jones, the Wallabies' coach when they lost the 2003 World Cup final to England in Sydney. "We've just got to lift the expectation of the players."
But he dismissed suggestions England and Australia could benefit from the world's five leading teams -- Ireland, France, New Zealand, South Africa and Scotland -- all being in the same half of this year's World Cup draw.
"I don't buy into that," said Jones. "Having been to a fair few World Cups every quarter-final is tough, every semi-final is tough, and every final is tough. So I don't understand that rationale."
The Barbarians will be captained by Wales great Alun Wyn Jones, who earlier this week announced his international retirement, having amassed a world record 170 caps.
Jones said the non-cap match was a chance for rugby union to showcase its "traditional values".
"I don't know how many caps Alun Wyn Jones has got," said Jones.
"We've got Kai Yamamoto who doesn't have a cap and can't speak English. To come together as a team and enjoy each other's company off the field and then play some good rugby on the field is really important."
