Cook's team were humiliated by 405 runs in the second test at the home of cricket as Australia levelled the five-match series 1-1.
"The crowd really get behind us here," Cook told a news conference on Tuesday. "If we get on top we feel as if we've got an extra man playing for us because of the noise.
"It's almost a different atmosphere to anywhere else we play. We are 1-1 in an Ashes series coming to Edgbaston, a fantastic ground where we know that if we play good cricket the crowd will get behind us.
"Lord's was an absolute disaster but that's gone. It's like a three-game series now and we need to win two of them to create something really special," Cook said.
England have rejigged their lineup, bringing in batsman Jonny Bairstow for Gary Ballance, and may also need to call up paceman Steven Finn in place of Mark Wood who has an ankle problem.
"With the rainy weather today Woody can't bowl outside so we're a little bit concerned about making a call on him," said Cook.
England have made a series of poor batting starts recently and the skipper is hoping the in-form Bairstow's inclusion and Ian Bell's promotion from four to three in the order can spark a turnaround.
"We've found ourselves three wickets down early on too many occasions in the last six months or so and we've had a little bit of a rejig," said Cook.
"Congratulations to Jonny, he's knocked the (selection) door down while playing for Yorkshire. He's averaging over 100 which is fantastic cricket at any level."
Cook had a warning for Chris Rogers despite saying he was pleased to hear that Australia's opening batsman was fit again after a dizzy spell forced him to retire in the second innings at Lord's.
Rogers feared he had suffered another bout of concussion following the head knock at training that ruled him out of both tests against West Indies but subsequent checks showed it was an inner ear issue.
"It's good that he's physically okay, we don't want anyone getting head injuries...but certainly we'll have to test him," Cook said.
(Writing by Tony Jimenez, editing by Ed Osmond)
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