Wales were beaten 20-19 in Saturday's third and final Test, having lost the previous two encounters 27-19 and 25-23 in a creditable series performance down under.
And having cut the margin of defeat on each occasion, Howley wants another crack at the Wallabies.
"Can we play them again next week please?" he quipped after Berrick Barnes' 75th-minute penalty inflicted late heartbreak on the tourists for the second week in succession.
The former scrum-half, deputising as coach because of Warren Gatland's injury, continued: "I am immensely proud of this group of players and there are a lot of good ingredients that have come out of the last three weeks that should make them feel pretty proud of their efforts.
"There were moments in the match we could have controlled better. But those moments will come again in the Autumn Series and the Six Nations and, hopefully, we will have learned how to make the most of them.
"A lot of things happened in the last 10 minutes and it was a new experience for a lot of these young players, who hadn't played in a three-Test series before. It has been a fantastic learning curve for us discovering how to get back up for games week in, week out.
"The respect we have had over here has been great, but this Welsh team is better than that. We want to win international games and the one thing you need to do when you gain respect is come to places like Australia and win."