The win heaped more torment on England who were beaten 5-0 in the five-Test Ashes series and now face defeat on a similar scale in the shorter form of the game.
Nathan Coulter-Nile took 3-47 as Australia restricted England to 243-9 after the tourists batted upon winning the toss and Warner and Marsh carefully managed a run chase that saw the home side win with 10 overs to spare.
"The first 10 overs we played alright and then we did what you can't afford to do, which is keep losing wickets and it's very hard to build momentum," Cook said.
"Everyone got 20 or 30 and you need to go on. The last match we got a big score. Someone gets 100 or 80 and you get 300 plus and that's what we needed."
More From This Section
"Obviously, they've won a lot of cricket against us over the last couple of months," he said. "It's tough to stop that. "We've got two games to try to do that. We've got to try to win a game."
Australia was never hurried and never lost its composure in its pursuit of England's total. While Warner scored his 71 runs from 70 balls with seven fours and two sixes, he wasn't always the dashing batsman he has been in the past.
Marsh then took control of the run chase and, in a patient and carefully measured innings, reached his 71 runs from 89 balls in 141 minutes. He had help from captain Michael Clarke who made 34 and veteran Brad Haddin who was 37 not out at the close.