The Royal Blues flew out to Greece to face the Greek side in Piraeus with Stevens pleading for caution at the start of a competition which they reached the semi-finals of two seasons ago.
They face Montpellier and Arsenal in their other Group B matches, but Stevens says the first hurdle could not get much higher.
"We know how strong they are in Piraeus," he said prior to departure. "You only have to look at their home games against German sides in the past.
"I don't think I am going to have to remind anybody what they did to Dortmund at the Karaiskakis stadium last year."
Schalke's bitter local rivals were beaten 3-1 a year ago, and given the way they walked away with the Bundesliga title in each of the last two years, that should say enough about the size of Schalke's task.
However, Stevens is also looking forward to measuring his side up to another European heavyweight at the start of a "challenging" group phase.
"We have spent long enough revelling in this Champions League qualification, but we have to put that behind us now," he said on the Bundesliga club's website.
"Now things are finally getting under way and we are looking forward to our group, which is very challenging."
Schalke warmed up for their Champions League debut with a 2-0 win at Greuther Furth on Saturday, a result which lifted them up to third in the Bundesliga.
Olympiacos have made an even more impressive start to the Greek Superleague season, though, with three wins out of three, eight goals scored and only two conceded.
They can buy little with their domestic form, though, and their coach Leonardo Jardim is counting on the home crowd to give them the edge tomorrow night.
"Of course we have got to make the most out of the fact we are playing at home," he said at the pre-match press conference.
"Usually when we play at home, we get the result we want, but we are up against a very strong side so we have got to keep our focus.
"Schalke have good players, but we have faith in our own team."
Jardim, who took charge of the club in the summer and only knows about the victory over Dortmund from the history books, says that result will count for nothing tomorrow.
"It is going to be a different game," he said. "It is good that we have the advantage in games against German opposition, but that will not help us in the slightest."
Although Giannis Maniatis and Pablo Contreras are both back from injury, Jardim is still without Avraam Papadopoulos for the clash, but his Schalke namesake Kyriakos Papadopoulos is part of the Royal Blues' travelling party.