The Australians trounced the Ashes holders by 381 runs in the opening clash at the Gabba for their first Test win over England in almost three years to make the early running in the five-Test series.
Skipper Alastair Cook admitted his England side were "totally outplayed" in Brisbane, but Clarke urged his team to stay grounded heading into what is shaping up as a crucial Test in the series on Thursday.
Clarke said the Australia side was a long way from being the team they wanted to be.
"I'm excited by the way we played in Brisbane. But, if you look at our results over the past 12 months, we have no reason to brag, or gloat or be over the top," he told reporters.
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"I think that's because everybody knows we're a long way from being the team we want to be. It's only one Test win and we've got some work to do in this second Test and throughout the series."
Clarke named an unchanged team for Adelaide, the first time he has been able to do so since the corresponding match last summer against South Africa.
"We looked at the wicket and thought about the extra bowling option with James Faulkner in the team," he said.
"We've seen through his career that his overs are crucial for this team. On good flat wickets like this wicket looks here I think his bowling is going to be very handy not just for taking wickets but also building pressure from one end.