Hamburg face dropping down from the top flight for the first time after a disappointing season saw them finish third bottom, just one point clear of automatic relegation.
They face Greuther in a two-legged tie and, although their opponents have only lost once in their last 14 matches, Slomka believes that his side are favourites.
"We want to cause them a surprise or two," he said. "We've prepared ourselves for Furth.
"This is a huge challenge for them, but they've played very well recently.
"We are the Bundesliga team and we are the favourites. We need to deliver on that.
"We need to play with a high tempo and play with energy and intensity. Tension can also be something positive.
"We played better in Mainz than the result suggested. But the games we've played recently mean nothing now. It's all about Furth."
The two sides meet for the first leg on Thursday at the Imtech Arena, with the return match on Sunday.
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
‘England have the players to win the World Cup – it’ll be tough for Thomas Tuchel to do a bad job, with the squad he has at his disposal’ Former Three Lions winger backs new boss after gentle qualifying draw
