They needed just 37 overs to bowl England out for a meagre 103 on Sunday's fourth day, paceman Mitchell Johnson leading the way with three cheap wickets, having set their arch-rivals a mammoth victory target of 509 runs.
Clarke's men produced a near-ideal display to level the five-match series at 1-1 after their 169-run loss, also inside four days, in the first test in Cardiff.
"That's why I think Chris Rogers and Steve Smith deserve a lot of credit.
"Obviously when we got a crack with the ball the boys executed really well and we continued that in the second innings."
However, Clarke added: "I think the other thing is to obviously be extremely happy with the way we performed but also respect that we've only played two test matches in a five-test series.
"I still see areas where we can get better, a few of us would definitely like to score some more runs, I'd like to see no dropped catches.
"So we turn up to training in Derby in a couple of days and we try and get better," said Clarke ahead of next week's three-day tour game which will provide Australia's lead-in to the third test at Edgbaston starting on July 29.