The Wallabies kick-off their Grand Slam tour against Wales at the Millennium Stadium on Saturday before taking on England, Italy and France.
"There's four massive hurdles to come," said Ashley-Cooper.
"We haven't spoken about an unbeaten tour but it's probably in the back of a lot of guys' minds. It's certainly in the back of mine.
"It's important that you just take it Test by Test and we've got two midweek matches as well so there's still six games to go.
"Our next hurdle's Wales and I think we've got to focus purely on that and then the result will take care of itself."
And Ashley-Cooper reckons his side's landmark triumph, after trailing 24-12, means the Wallabies are starting to believe they can beat anyone in any situation.
"It's a big step," added Ashley-Cooper.
"We're making progress each game, we're taking little steps and that was a step we needed to take and one we all believed that we could make.
"It's important not to get too caught up with that. But it has created a lot of confidence and belief and momentum for the start of the tour.
"It's certainly going to do us the world of good knowing next time we approach the All Blacks it's next year in a World Cup year.
"So it's done a lot for us, the monkey's off our back and we're back to even."
Memories of last year's failed Grand Slam tour is also in the back of some minds, however.
"It would be nice to correct that but that's behind us now. It was such a disappointing tour and everyone was pretty upset by it but I think it's important just to look forward at what's ahead and don't reflect too much on the past.
"We can't afford to create any doubt now, we've got our momentum and the mood's really good."
And Wallabies coach Robbie Deans is expecting a fired up Welsh outfit when the two sides meet on Saturday.
"They'll be smarting from our last visit there," said Deans.
"They'll have us in their sights. They'll be lying in wait, their first outing of their international season, excited as hell."