The tourists head into a fifth and final Test at The Oval starting Thursday, 2-1 up after last week's Old Trafford washout denied a dominant England the chance to claim a series-levelling win.
Australia, as the holders, are assured of retaining the Ashes.
But the goal of a first Ashes series win away to England since 2001, a run that spans five tours, remains in their sights.
Australia were 2-1 up heading into The Oval four years ago only to pay the price for some over-exuberant celebrations before they arrived in London as England fought back to square that series 2-2.
Fast bowler Cummins said the circumstances were different this time and that ending a 22-year wait for an Ashes series win in England would be the ideal way to finish a tour that started at The Oval with Australia's victory over India in the World Test Championship final.
"I think the good thing is that it's a really similar group to 2019," Cummins told a pre-match press conference at The Oval on Wednesday.
"That Manchester (in 2019) was a big win to retain the Ashes, which we hadn't done for a long time off the back of Headingley, even Lord's, where we probably missed a trick last series.
"I felt like that was a big exclamation mark on the end of that series with still one Test match to play."
'Not at our best'
He added: "It feels really different here, this group has been really motivated to win the series.
"We know that it wasn't our best week last week and at the end of the game it was a bit of a pat on the back, 'well done, we've retained the Ashes' but really it feels like the job's not done."
The upcoming match could mark the end of an era for an Australia team. Several players are 30 or older, although under-pressure opening batsman David Warner, 37 in October, quashed rumours Tuesday he is set to retire, insisting he intends to stick to his plan of finishing on home soil early next year.
"It's a hard one," said the 30-year-old Cummins when asked about managing a transition from one generation to the next. "I certainly don't want to rush anyone out of the door."
He added: "I think this is about the fourth Ashes series where (England veteran paceman) Jimmy Anderson has said it's going to be his last one, so you never quite know."
Cummins's captaincy was criticised after England's three-wicket win in the third Test at Headingley was followed by Australia's pummelling at Old Trafford before rain came to their aid.
Mark Waugh, the former Australia batsman, suggested the cares of captaincy had made Cummins look "tired and frazzled".
"Is Pat Cummins the right man for the long-term captaincy?" Waugh asked on Fox Sports.
"Because when it's tough I don't think he is. I think he's OK when it's easy and he doesn't have to think too much, but it's a real question mark."
Cummins, however, received support from Ben Stokes on Wednesday, with the England captain saying of his rival skipper: "I'm not sure why someone would say he should give it (the captaincy) up.
"I don't know who has made those comments, but I think he's done a great job for Australian cricket. It's probably a little bit unwarranted from whoever said that - and that's coming from an Englishman."
