After the tension and drama of Trent Bridge, the action at Lord’s was more heavily skewed in the home side’s favour, with 10 more Australian wickets on day four delivering a mammoth 347-run win.
Both matches took place in quick succession in uncommonly draining conditions and Cook was delighted to join his side in a celebratory drink at the home of cricket.
But while the problems for the tourists mount up both on and off the field, Cook insists his side will not be taking their ailing opponents lightly despite growing predictions that England could deliver a dream 5-0 result.
“I think we’re going to have a few quiet beers in the dressing room. It’s a very special moment when you win a Lord’s Test match against any side but against Australia... they are the times you cherish as a player,” he said.
“However the lads want to enjoy themselves (is fine) and then we’ll come back on Monday ready to work extremely hard for two more (back-to-back) games.
“It’s a good dressing room to be in, we’ll enjoy this.
“Then we’ll come back at Old Trafford and see how we can go about winning that game.”
England were memorably victims of a 5-0 whitewash Down Under in 2006-07 and the number of former England players, led by the bullish Sir Ian Botham, predicting a reverse result this time around has picked up noticeably in recent days.
Cook, though, was eager to stress that any such result is a distant consideration for the current generation, whose focus remains firmly set on sealing a series win when the teams reconvene in Manchester on August 1.
“It’s certainly too early for that (whitewash talk),” said Cook.
“You only have to look at our dressing room to see how hard we’ve had to work to win these two games.
“At certain moments in this game we were right under the cosh so it’s huge credit to the lads that we’ve managed to pull through.”
England’s man of the match was Yorkshire’s Joe Root, who scored a maiden Ashes century of 180 to confirm he is well at home in his new position at the top of the order.
He also refused to be kept out of the game as the last rites were delivered, backing up senior spinner Graeme Swann’s four wickets with the scalps of Michael Clarke and Usman Khawaja.
Root continues to impress in whatever role England ask him to fulfill and Cook was full of praise for the 22-year-old.
“We spend most of our time talking about him don’t we?” said Cook.
“He’s taken to international cricket extremely well because he’s got the right character.
“He adapts his time to whatever is required. In a high pressure situation to score a big hundred is a huge credit to him.
“He can be mighty proud of his performance in this game.”
Match report: Page 4.