The tourists were regarded as hot favourites before the start of this summer series, but Cook’s side out-bowled and out-thought their rivals to wrap up a 169-run triumph with one day to spare.
Cook, who came in for fierce criticism after their whitewash Down Under in the last series in 2014, told the Sky Sports Ashes channel: “It was a brilliant performance. The one-day and Test series against New Zealand was exciting and people appreciated the way we went about it.
“But this Test couldn’t have gone any better and we’ll enjoy tonight. Joe Root was fantastic and the bowlers were superb.
“Everyone was talking about what’s gone on in the past, but this is a different side. We had to look forward. We always took the attacking option in this game.
“We have four or five experienced players and the rest are inexperienced in terms of Ashes cricket. It helps when you’re on top and it’s been a really good four days.
“Hopefully we’ll come back and put in another good performances at Lord’s (in the next Test).”
After setting Michael Clarke’s team a target of 412, England skittled them out for 242 on day four to secure a 1-0 lead in the five-match series with Stuart Broad and Moeen Ali both sharing three wickets.
There was no stopping man-of-the-match Root who took two of the last three wickets, including Mitchell Johnson who had briefly threatened with a lively 77, to add to his knocks of 134 and 60. He also finished the day by catching Josh Hazlewood off Moeen Ali to set up the wild celebrations at the SWALEC Stadium.
On Root’s stirring first innings, Cook added: “The world is his oyster with how good he is but you don’t get there without hard work.
“We were 40-3 and to score 134 in an Ashes series when the tension was high was fantastic. Our bowlers were superb though on a pretty slow wicket.”
Hard work was something England were not accused of by some of the country’s media as they headed to Spain for the Ashes build-up while the Aussies tested their skills against Essex.
However, Cook, whose acrobatic catch saw the demise of Brad Haddin, said; “Catching was something we worked hard on over there. Alongside the golf the catching was very important.
“There were some very sore hands. Some called it a holiday, but it’s just great that hard work paid off.”