The tourists slumped to a 381-run defeat in front of a hostile crowd at the Gabba, where an occasionally spiteful contest re-ignited the debate about sledging and sportsmanship.
Australia captain Michael Clarke was fined 20 per cent of his match fee after he was caught by a stump microphone telling James Anderson to get ready for a "broken" arm when the paceman was batting, one of a number of heated moments during the Test.
Australia have pledged to maintain the aggression at Adelaide Oval when the match starts Thursday, but Cook struck a more statesmanlike tone.
"I think it's important that both sides recognise that a couple of scenes in that last Test weren't great for the game of cricket," he said.
"It's important that we play in the right way. I think people what to see real tough cricket, that's what they enjoy, especially between England and Australia, but there's got to be a boundary that we don't cross.
"Maybe last week we let emotion get ahead of ourselves a little bit on some occasions and it got a little bit ugly.
"Obviously Michael and I have a responsibility as captains of both sides to make sure that doesn't happen."
Far more than taking on a team, England's campaign to win a fourth consecutive Ashes series has at times felt like a battle against an entire nation, with unsympathetic crowds and an orchestrated media campaign joining forces.
Following a Brisbane newspaper's front-page attack on England paceman Stuart Broad on the opening day of the first Test, Adelaide's "Advertiser" has sought to embarrass the team by publishing a picture of English cricketers out on the town at 3:30 in the morning.
Wednesday's paper accused the team of snubbing a dinner held by the state cricket association.
Adelaide Oval is sold out for the opening days and local fans are likely to give England another frosty reception.
Cook said it was nothing he had not seen before.
"Obviously you let your cricket do the talking," he said.
"Last time we had the same hostile environment when we got here, but towards the end of the series we played some really good cricket and that hostility changes because everyone was very respectful of the way we played.
"In that last game we didn't do ourselves justice and they got on top and that's what home supporters do what you get on top.
"We knew that coming into this series and a few of us have played a lot of cricket over here. We know how important it is to let the skills out in the middle do the talking and everything else will take care of itself."
England have lost batsman Jonathan Trott, a linchpin of the victorious 2010-11 Ashes tour, but Cook was tight-lipped about his replacement at number three in the batting order -- as he was for all his team's selections.
Joe Root or Ian Bell are expected to move up from the middle order to replace the South Africa-born Trott, who left the tour to deal with a stress-related illness after failing twice with the bat in Brisbane.
Selectors will pick from either Jonny Bairstow or the uncapped duo of Ben Stokes and Gary Ballance to slot into the middle order, while Tim Bresnan is favoured to come back into the side at the expense of fellow seamer Chris Tremlett after recovering from a back injury.
Adelaide Oval's new drop-in wicket is expected to favour batsmen and exact a big toll on fast bowlers, raising speculation Monty Panesar might be picked as a second spinner to partner Graeme Swann.
"I think it is a realistic option," Cook said.
"That's one of the things about home advantage, is that you know the wicket better than the opposition. So we have to use all our experience to make sure we pick the right side."