The Dortmund midfielder admits that his side are hungry for Champions League success after finishing last season as beaten finalists
Dortmund were defeated finalists last year in Wembley, succumbing to a 2-1 loss to rivals Bayern Munich.
Grosskreutz admits that the defeat has weighed heavily on him and his team-mates, but, they are now better equipped to put right that disappointment.
"Whoever's been to the final and experienced what was going on, wants to go there again," the 25-year-old said in an interview with Sport 1.
"But that's still a very, very long way off. We need to stay cool and get through the first round.
"We have played convincing and really good football. The other teams are warned in any case, but it is about us. We need to do our thing, then, it will be hard to beat us.
"We are calmer on the ball [than we used to be] and, we are even more composed when the game is still tight. We are good and compact and, due to our individual quality, we know we can always score a goal."
Jurgen Klopp's men were drawn against Arsenal, Marseille and Napoli in Group F in Thursday's Champions League draw.
"I was hoping for an English team so Arsenal is good," Grosskreutz continued.
"From Pot 4, I would not necessarily have wanted Napoli. But in the end we go wherever we have to."