Having collected wooden spoons in coach Dean Bailey's first two years at the helm in 2008-09, Melbourne showed significant improvement last year, winning eight games to finish 12th.
With an exciting and rapidly developing young list, there is hope among fans of a Demons finals appearance in 2011.
Green understands the reason for the excitement, but said the club will focus only on winning games week-to-week.
"You always have expectations going into any season and given where we are as a club, and where we've been over the last few years, there's going to be a high demand that we improve and get better," he said at the gathering of all AFL club captains at Etihad Stadium on Thursday.
"We go out every week to win games of footy and I'd hope that starts with Sydney in round one."
Green said the talk surrounding Scully, out of contract at the end of this season and believed to be a major target of new club Greater Western Sydney, would not affect the playing group.
"That's something that's going to be more of a media thing rather than a club thing," he said.
"As a club, Tom's going to get on with his footy, we're going to be there for him and support him, and hopefully he gets out there and plays his best footy this year, which we know he will."
The 30 year-old, entering his first season as skipper after 11 years and 220 games with the Demons, said the new role would be an exciting learning experience.
"Today is one of these days where you meet all the other club captains and you look at them and think, 'gee, they're all great players and great leaders'," he said.
"Hopefully one day I can look at it and think, 'I'm there now'. And that's what I've got to do to lead this club.
"I'm still learning my leadership style and how to be a captain, and that won't stop until the day I retire."
Green believes the club's list is in good shape approaching the round one clash with the Swans, with Cale Morton (finger), James Frawley (pectoral) and Jordie McKenzie (groin) the only players from Melbourne's strongest line-up set to miss.
He forecast a round two or three return for Morton, who ruptured the flexor tendon in his ring finger in a training mishap on the eve of the NAB Cup, and a similar return date for Frawley.
The 2010 All Australian defender had surgery after tearing his pectoral muscle while weight training in January.
"James has been told he can play round two, so at least neither of them are going to miss huge chunks of the season, and that's great," Green said.
Brad Green is a $409,000 forward in the Toyota AFL Dream Team competition.
