Hamburg are the only club to have played in all 51 seasons of the Bundesliga but after last week's 3-1 loss at Augsburg, the north German club have slipped five points from safety ahead of a clash with champions Bayern Munich on Saturday.
The northerners will complete their league campaign with a trip to Mainz, who could still be chasing UEFA Europa League qualification on the final day.
"The lay of the land's pretty obvious when you're up against FC Bayern," Slomka said on Friday.
"But obviously we're going to go out there and give it everything we've got.
"We want to try to get right on top of them, make it as uncomfortable as possible and look to create the odd chance of our own."
Stuttgart (32 points) sit ahead of Hamburg (27) in the last safe spot in the Bundesliga with Nuremberg (26) and last-placed Eintracht Braunschweig (25) able to overhaul Slomka's men if they lose to Bayern.
But Slomka conceded his team are far behind Pep Guardiola's champions.
"Bayern absolutely dominate the Bundesliga," Slomka said.
"A point from the game would be a huge surprise and a win a sensation against them.
"If we want to cause a sensation, we're going to have go to the very limit."
If Hamburg defeat Bayern, and Nuremburg and Braunschweig lose to Hannover and Augsburg respectively in the penultimate round, Slomka's side will avoid automatic relegation but may still have to compete in the play-off.
