A 3-1 defeat to Lazio in Rome completed a 5-1 aggregate defeat to see Bruno Labbadia's men crash out of Europe in the last-16.
Their focus now turns to the Bundesliga, where poor recent form has seen them fall out of the race for a place in Europe and into risky territory with just nine games of the season to go.
"It's important we now find our feet in the Bundesliga," said Labbadia. "We have had some very tight results in recent weeks without being able to win them and we're still lacking something.
"We have got to get points at all costs."
The defeat to the Serie A side was an important lesson to Labbadia's men, who had more shots on goal than the Biancoceleste yet still slumped to an emphatic defeat.
"We have got to take out of the game against Lazio that we have got to be stronger and more certain in defence," he said.
"And we've got to take our chances better."
Vedad Ibisevic returned from suspension to face Lazio while Federico Macheda put in one of his best performances for the club so far in an uncustomary position wide left, where Ibrahima Traore could return tomorrow.
Stuttgart will come up against Armin Veh, the coach who last led them to the Bundesliga title in 2007.
"I know Stuttgart very well," said the Frankfurt coach. "They certainly have the aim of being one of the leading sides, which they aren't managing at the moment.
"But it's tough when you are involved in three competitions. Stuttgart are always capable of playing really good football and they have done better away from home this season than at home, so I don't necessarily think it's an advantage that they are coming to us."
The Eagles have also lost their way a little recently and they dropped out of the top four for the first time all season last weekend.
"That makes it very important for us to win at home again because we want to stick in there at the top," added Veh, who has Bamba Anderson back in his squad and in contention for a place.