Victory meant England had won three of their four November internationals, with the lone loss an agonising 16-15 defeat by world champions New Zealand.
In January, Jones had his England contract extended until 2021 – two years after the 2019 World Cup in Japan.
But the experienced coach had his position called into question by a run of five straight defeats that spanned the Six Nations and the start of England's tour of South Africa in June.
England stopped the rot, however, with a 25-10 win over South Africa in the third and final Test, although the Springboks won the series 2-1.
"I think we took steps forward in South Africa," said Jones.
"We'd had a tough Six Nations. We'd got some things wrong in planning, some things wrong in terms of where we were going as a team and we needed to regroup and we did that," he added after Saturday's win over the Wallabies at Twickenham.
"This (November) series was a step forward and the 2019 Six Nations will be another step forward again."
England's next international will be the toughest assignment European rugby has to offer – a Six Nations opener away to defending Grand Slam champions Ireland, who this month succeeded where Jones' side failed by beating the All Blacks 16-9.
Asked if he felt confident ahead of the Dublin clash on February 2, Jones replied: "Yeah, 100 percent."
Jones, with England missing several injured players, was also enthused by the depth of talent at his disposal.
"We've got great competition. Consider today, we played without Mako (Vunipola), (Ellis) Genge, (Joe) Launchbury, (George) Kruis, Billy (Vunipola), (Chris) Robshaw, (Anthony) Watson, (Jonathan) Joseph, (Jack) Nowell, (Chris) Ashton. That's for starters.
"To be the best in the world you've got to push hard."
England wing Jonny May opened the scoring with a try in just the second minute on Saturday.
But Australia fought back to level the match at 13-13 come half-time, with the Wallabies unfortunate not to be leading at the break after South Africa referee Jaco Peyper controversially awarded a penalty rather than a penalty try following a 'no-arms' challenge by England co-captain Owen Farrell on lock Izack Rodda.
England, however, pulled clear in the second half by scoring 24 unanswered points, including converted tries from fullback Elliot Daly, wing Joe Cokanasiga and Farrell.
Fly-half Farrell converted all four of England's tries and also kicked three penalties in a match haul of 22 points.
This was just Cokanasiga's second Test and Jones jokingly said: "He's still got his training pants on. Wait until he gets proper pants. He'll be able to play a bit."
Reflecting on England's improved showing after the interval, the coach added: "First half, we had opportunities to get a bit further ahead than we were, missed those and allowed them back into the game.
"Second half, we were able to regroup, play in a real English way and I was really pleased with that."
Saturday's result meant England had won all six of their Tests against Australia since Jones was appointed after the Wallabies condemned them to a first-round exit at the 2015 World Cup with a 33-13 victory at Twickenham.
But Jones, in a week that marked the 15th anniversary of the Australia side he coached losing the 2003 World Cup final to England, was unconcerned.
"It's not about playing against Australia. It's about us. I love coaching England and love English players," he insisted.
"It's about us getting better as a team. It wouldn't matter if we were playing Argentina or Afghanistan, all we want to do is play good rugby.
"I've got no interest in just beating Australia or having a good record against Australia."AFP