"We're delighted with the way the bowlers bowled, and it was a good effort from the batters to chase down that score."
Developing a winning habit early in the tour was one of England's goals on arriving in Australia and the manner in which they went about their run-chase at the Waca Ground was a reflection of the confidence within the camp.
After Cook's early dismissal, bowled by Michael Hogan after planting his front foot down the track and shaping to play the ball to leg, Strauss took charge and was well supported by the other members of the top order.
The 33-year-old England captain shared stands of 65, 66 and 54 with Jonathan Trott, Kevin Pietersen and Paul Collingwood - before he and Ian Bell, who finished with 22 not out, knocked off the remaining runs.
Graeme Swann got plenty of overs under his belt on the final day in Perth
Trott was caught behind down the leg side for 23 off the last ball before tea, Pietersen fell leg before wicket for 35 when he attempted a reverse sweep and only Collingwood, who was caught for 26, did not look comfortable at the crease.
Strauss, meanwhile, was particularly strong on the back foot, relishing the chance to pull anything dropped short, but he brought up his century with a straight drive off spinner Michael Swart.
Strauss is certain to be targeted by Australia's attack when the Ashes series begins in Brisbane on 25 November, so his innings was an important signal of intent.
England also bowled well earlier in the day, picking up nine wickets for 114 runs after Western Australia had resumed on 109-1.
There were two dropped catches - Bell failing to hold an early chance offered by Swart at gully and Collingwood putting down Luke Pomersbach at slip - but that did not take any gloss off the overall performance.
And England were especially delighted to get rid of Marcus North, the only member of Australia's Test side involved in the match, for a single, run out by substitute Eoin Morgan after being called for a sharp single by partner Adam Voges.
Opener Wes Robinson made his second half-century of the match for the home side, but soon after was lured forward by Swann and stumped by Matt Prior for 54.
Swann also removed the aggressive middle-order pair of Pomersbach and Luke Ronchi before adding the wicket of Michael Beer, but he was not amused by being hit over the top three times by last man Hogan, who made 21 off 12 balls before running himself out.
Strauss added: "It's important we play well and win as many of these games as possible, it's also important that batsmen get used to the conditions.
"The best way to do that is by spending a lot of time in the middle. It was satisfying to get a hundred and see the guys home, but I'm sure there are sterner tests ahead."
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