We're taking the urn home so that's certainly what we came to do: Tim Paine after defeat in 5th Test
The tourists came into the match at the Oval seeking their first series victory in England since 2001 but came up short, losing by 135 runs on Sunday.
But Paine said Australia, who won at Edgbaston and Old Trafford but lost agonisingly to a Ben Stokes-inspired England at Headingley, had achieved their main objective in retaining the urn.
"We're taking the urn home so that's certainly what we came to do," he said. "We're thrilled by that, a little disappointed by this game obviously, puts a bit of a dampener on it."
"We can be really proud of the way we've come over here, which is a challenging place for Australians to come and play and win," he added.
"To win two Test matches pretty convincingly, should have won a third (at Headingley) -- let that slip no doubt."
Paine said winning the first Test at Edgbaston, where Australia triumphed by 251 runs, had been crucial for his side's confidence.
"There was so much talk about that being a fortress and how difficult a place it was going to be for us to start the series, probably by design, so for us to come over and win that first Test, and win it, in the end, quite convincingly gave us the belief that we could do it," he said.
And the skipper said he still felt he had a role to play in taking the side forward.
"We've still got a way to go," he said. "Obviously Steve (Smith) had an unbelievably good series and won us a couple of Tests by himself so we've got some parts that we need to improve.
"But if we click them into gear while we've got Steve at the height of his powers and with the pace attack we've got, in the next few years we're going to be a very hard team to beat."
"There's plenty of improvement in this side," Paine added.
"I still feel I've got a little bit to give in that space and we're always trying to develop more leaders within our group as well."
Smith, who scored 774 runs in just seven innings, said he was exhausted after a long tour, which also included the World Cup.
The former captain, who returned to international cricket in June after a ban for ball-tampering, received a standing ovation from the crowd in south London when he was out.
"It was a nice reception as I walked off," he said.
"It would have been nice if I'd had a few more runs under my belt in this game.
"I've given it my all since I've been here for the last four-and-a-half-months in every Test match that we've played and I didn't have much left to give today.
"I'm pretty cooked to be honest, mentally and physically. I'm looking forward to a nice couple of weeks' rest now before getting into the Australian summer."