But he insisted Joe Root could join him as a victorious England captain "Down Under" despite the lack of "absolute clarity" regarding the composition of the side just a week ahead of an expected squad announcement.
England may have enjoyed series wins over South Africa (3-1) and West Indies (2-1) but they ended their home Test campaign pretty much where they started it – with doubts over the identities of numbers two, three and five in their batting order.
Tom Westley has yet to convince at number three, having made five successive single-figure scores prior to a 44 not out in a modest and victorious run chase against West Indies at Lord's this month.
Dawid Malan has fared better at number five without nailing down a place while Mark Stoneman is the 12th opening partner Alastair Cook has had since Strauss himself retired five years ago.
"There are going to be opportunities there in Australia for guys to make a very strong case for a long-term England career based on performing well when it really counts in Australia," Strauss, the England and Wales Cricket Board's director of England cricket told reporters at Trent Bridge on Wednesday.
"I’d be lying if I said we were going to Australia with absolute clarity on what our best XI is. We’re just not in that position at the moment."
Turning to the problems England have had in filling his old position, Strauss said: "I would resist any narrative that says we have been chopping and changing willy-nilly.
"I think the reality is the secret to a long England career is not how good you are, it is how consistent you are and those guys have not been consistent enough," he added.
Nevertheless, Strauss – who led England to a 3-1 Ashes triumph in Australia in 2010/11 – is adamant Root, for whom the Australia tour will be his first overseas assignment as a Test captain, could match his achievement.
England will be desperate to exact revenge for the 5-0 drubbing they suffered in Australia in 2013-14, even though they wrested the Ashes back on home soil in 2015.
Australia too have concerns about the make-up of their side, both when it comes to their batting and the fitness of some key fast bowlers.
"The reality is there are two teams with really strong assets and some vulnerabilities," said Strauss.
"Our challenge is to start the tour well. If we start well, hit the ground running and some of those guys who have not played a lot of Test cricket get an early score, then I think we are in a great position to win."
As for what lies in store for Root in Australia, Strauss said: "It’s the biggest challenge an England captain will ever have.
"There’s all sorts of reasons for that. A lot of them are off-field. You are living in this incredible bubble for a long period of time, everything is directed towards you as England captain in terms of being responsible for what’s happening on the pitch.
"But also the conditions in Australia are very changeable from one venue to another, to different periods in the game, and you need to be able to adapt to those conditions you see in front of you.
"That is why at the back end if you are able to win -- certainly for me it was my greatest moment as an England captain, and I think Joe will be incredibly motivated to do that early in his captaincy career.
"He's got a great chance, he's got his own way of thinking about the game and that will stand him in very good stead in Australia."
The first Ashes Test takes place in Brisbane from November 23, with further matches to follow in Adelaide, Perth, Melbourne and Sydney.