Cook's team concluded their dominant 3-0 series win over the Australians with a dramatic draw in the fifth Test at The Oval on Sunday and thoughts have already turned to the next instalment of cricket's most enduring grudge match.
England, set a target of 227 to win after Australia captain Michael Clarke's bold declaration, needed 21 more to win off 24 balls with five wickets left when the umpires decided the light, even with the floodlights on, was too dark to continue.
The draw meant England have now triumphed in three successive Test series against Australia for the first time since the 1950s.
And Cook, delighted with the way his team coped with the pressure of being favourites, believes his battle-hardened troops will have no problems dealing with the renewed challenge from Clarke's men in the rematch.
"If you go right back to the start of the series a lot of questions were asked of the England team and people wondered if we would be able to handle the pressure of being favourites. To be able to deliver on that means we can enjoy a few well deserved beers," Cook said.
"We've had some tough times but we've shown character. When runs needed to be scored and wickets need to be taken we've done it.
"That's the hallmark of a good side, Even when the opposition scored nearly 500 here we can force our way back into the game.
"We are becoming incredibly tough to beat. We are forcing our way back into games and that comes with experience."
Cook knows Australia will come at England hard on enemy territory in the year's second Ashes series, which starts in Brisbane in late November.
But he is certain his squad can cope with anything the hosts throw at them.
"In Australian conditions where they are more comfortable of course it's going to be hard, that's why Australia is such a hard place to go. But I feel very comfortable that this side is capable of doing that," he said.
"You earn the right. You look at our side and there is a lot of experience and knowledge that they are world class and will deliver when it matters.
"We have been through some tough times and good times and we know when to draw on it."
A rancorous series reached an explosive finale during The Oval Test as Australian coach Darren Lehmann accused England bowler Stuart Broad of cheating when he failed to walk despite a clear edge at Trent Bridge earlier in the series, while both teams were caught sledging.
However, Cook shrugged off talk of bad blood between the sides, claiming the war of words was the inevitable result of two teams so desperate to win.
"It's been an interesting series in that way. It's been hard, tough cricket and no side has been prepared to give an inch," he said.
"It's water off a ducks back. You can say what you want. The guys in the other side are entitled to their opinion.
"What's important is how we concentrate on what we do."
After watching Michael Vaughan and Andrew Strauss, his predecessors as England captain, lift the famous replica Ashes urn over the last eight years, it was finally Cook's turn on Sunday and the Essex batsman said: "It's an incredible feeling, one that unfortunately happens so quickly after such a long build up in your mind. It's what dreams are made of."
While Cook savours the best moment of his career, England's star performer Ian Bell warned his team-mates not to get complacent.
Bell, who scored 562 runs at 62.44 with three hundreds during this Ashes campaign, said: "Going into the series we would have taken 3-0 and it's left it well posed going into the series down under.
"But as a group we play our best cricket taking it a game at a time. If you get carried away or look too far ahead it bites you on the ar*e."
Bollywood celebs show you colours for Navratri 2017
Photos: Kareena Kapoor Khan, Kangana Ranaut at the Mumbai airport
Birthday special: Chris Gayle and his multiple records in cricket
In Pictures: 17 dreaded on-screen villains of Bollywood
'Ramayan' director's great granddaughter Sakshi's hottest photos