Australia lost the Oval Test by 49 runs and allowed England to level the Ashes 2-2.
Chasing 384 to win, the visitors got off to a brilliant start as the duo of David Warner and Usman Khawaja added 140 runs for the opening wicket.
However, game-changing spells by Chris Woakes (4-50) and Moeen Ali (3-76) on the final day denied Australia their first Ashes win away from home since 2001.
Although Australia retained the urn for a fourth straight series, Cummins was left to rue missing a golden opportunity of clinching the series after taking a 2-0 lead.
"We just missed what we were hoping to come over here to achieve, but to win the World Test Championship and retain the Ashes is a pretty successful tour," Cummins was quoted by cricket.com.au.
"Coming over here and retaining the Ashes feels like a bit of a missed opportunity. But in 2019 we were all pretty happy about retaining the Ashes. So don't think we should lose sight of that. Think it's a huge achievement to come over here and win and get ourselves into many winning positions.
"Once we reflect on it, we'll be proud that we were able to retain the Ashes, it's been a wonderful tour, but we all turned up today hoping to get up and win 3-1," he added.
Reflecting on the Ashes 2023, Cummins said the series could have been in their favour if they had capitalized on a few key partnerships.
"Think there are a couple of key partnerships batting-wise that felt if we'd just put on another 50 runs that it could really have turned the tide in our favour.
"No doubt that the one big innings they put on [at Old Trafford], you look at could we maybe do some things a little differently, but you never know if that will change anything. There are too many unknowns," said Cummins.
"Felt like we got ourselves into some really good positions, first of all winning the first two games, but then Headingley and again this week -- match-winning positions we didn't quite capitalise on. That happens. We were out of it in Birmingham and found a way to win," he remarked.
The 2023 edition of Ashes produced a riveting contest between bat and ball and Cummins hoped that they have managed to inspire a new generation to take up the sport.
"Everyone's been amazing and just been talking about the cricket and how much they loved, and I know it's the same back in Australia – big viewers and lots of people interested in cricket. I was a bit young for 2005 but that series gets talked about a lot, and it feels like this series might be the same.
"I really hope we've inspired a new generation. I look back to 2005 and what that series did for me as a young person, and I really hope there's someone who's the age I was then and says: 'That's what I want to be doing when I'm 21 or 22'," the Australia captain said.