The Reds have made no secret of their desire for a third straight campaign of European football next year, but that is now in jeopardy after Saturday's heavy loss.
"We know that we have got to win at all costs," said Slomka at a press conference. "We have got to perform much better and be stronger in the tackle.
"We have to keep compact, and then the goals mostly come anyway given our quality."
Indeed, Slomka, who will be without the injured Mohammed Abdellaoue and the suspended Lars Stindl, is focusing on resolving his side's defensive woes.
"We cannot afford to drop any more points in our situation," he added. "We have all got to defend better as a team."
Didier Ya Konan should be back for the Reds to replace Abdellaoue.
Furth are without Sercan Sararer, who is suspended, but they still make the trip north searching for only their second win of the season.
"We have shown often enough that we can be competitive, yet we would have hoped for more points," said their coach Mike Buskens.
"We will give it another go tomorrow to get our second win of the season."
A draw with local rivals Nurnberg at the weekend means Furth will go into the game with renewed confidence, but Buskens has warned his team to expect a backlash from Hannover.
"After losing two games in a row, they are going to be desperate to get out of this spiral," he said.
"Therefore, we are going to have to get at them right from the beginning."