The Cottagers have picked up only four points from their opening eight matches, and their next run of fixtures as domestic action resumes does not get any easier.
Following Sunday's visit of Everton, Parker takes his side to pacesetters Leicester and then Manchester City, before hosting defending champions Liverpool on December 12.
After such a daunting schedule, it would perhaps seem inevitable to find your team entrenched in the bottom three with little hope of progress.
Parker, though, feels tackling the elite head on is something to be relished as last season's Sky Bet Championship play-off winners look to prove themselves all over again.
"They (fixtures) don't (get any easier), but this is the division we are in and we all understand that," the Fulham manager said.
"We knew that at the outset and as a team understood the challenge we faced this year.
"The fixtures coming up are big ones, tough ones – but after these five or six, we will go into another five or six and I will get asked the same question and you will get the same answer.
"We are eight games into the season, we have had some real challenges and tough games along the way – and that will be the same story throughout the season.
"I am looking forward to the big challenges in front of us, but as a team we need to rise to that and embrace that."
Parker added: "Since the transfer window shut and players came in, there has been a real understanding on 'this is where we are'.
"We had a quick pre-season and a quick turnaround, hopefully now the players are understanding (our work) a little bit more, understanding the league and what is needed from them."
Everton opened the new campaign with four straight Premier League wins to climb to the top of the table but lost three in a row before the international break.
Parker rejects suggestions Carlo Ancelotti's squad will offer anything less than the sternest of tests.
"Carlo Ancelotti is an incredible coach," the Fulham boss said.
"His CV and what he has done in the game as a manager speaks for itself, so it's not a surprise in any way that he has gone in at Everton and is doing as well as they are.
"They have invested and bought very well in the summer. They have got a real good strength and balance in terms of what they are about.
"I am not surprised where they are because they have got a manager there who is world class. Likewise with their squad, there are some fantastic football players."