The Cottagers kick-off their season with a trip to Portman Road against Mick McCarthy's Ipswich, before clashes with Wolves, Derby and Cardiff, all within the first month of the campaign.
The former England international told the club's official YouTube channel: "If we can get off to a good start, then it will put us in good stead to push on.
"Ipswich is a tough first game, away from home too. They have a very good squad, they've been in this division for a while now and they're under a very good manager. We hope to get a positive result which can springboard us on to carry on doing well.
"It's been a tough pre-season but the excitement is building now. There's been a lot of training sessions but they have got us to where we are now in the few days before the start of the season."
After relegation from the top tier, Felix Magath has let over 20 players leave the club, bringing in Championship pedigree, including last season's top scorer in the division, Ross McCormack, from Leeds.
Magath also arrived at Fulham with a reputation of making training sessions extremely testing.
Parker, who has over 450 professional career appearances, added: "The fitness work has been hard at times but everyone has pulled through it, we're all fit and it has put us in good stead for the new season.
"The squad's practically different from last year's, there are a lot of new faces. Everyone's getting to know each other now, that's been helped by our two tours to Scotland and Austria so we've spent a lot of time in each other's company so it's going well.
"The lads are just raring to go now and looking forward to what will be a tough campaign."