The Bundesliga side dominated the play but struggled to create clear-cut chances as their hopes of a winning start to Group J were thwarted.
Klaas Jan Huntelaar, who scored four in the club's 6-1 second-leg play-off win over HJK Helsinki which booked their place in the group stage, had their best chance but failed to add to that tally as he thumped his shot from inside the area against the bar.
The Royal Blues provided the stand-out result of last season's Champions League with a 7-3 aggregate win over defending champions Inter Milan in the quarter-finals, including a stunning 5-2 win at the San Siro.
But Ralf Rangnick's men failed to hit those heights in rather less high-profile surroundings as Israeli side Maccabi Haifa took early lead in the group thanks to their 1-0 win over AEK Larnaca.
Schalke's Romania forward Ciprian Marica perhaps had more reason than most to be fired up for the contest, having been born in Bucharest and started his career with Steaua's capital rivals Dinamo.
And the 25-year-old, signed in the summer from Stuttgart, had the game's first chance as he fired over the bar from the left of the area.
Schalke's attacking line-up, which featured Raul, Huntelaar and Jefferson Farfan, was always going to cause the hosts problems and the veteran Spaniard, more used to the Champions League than the Europa League, had a header from six yards tipped round the post by Steaua goalkeeper Cristian Tatarusanu in the 35th minute.
The Royal Blues were looking the more dangerous, but were struggling to break down a stubborn Steaua backline.
Huntelaar had a shot blocked by Pablo Brandan just before the break and the Dutch striker almost broke the hosts' resistance midway through the second half only for his drilled effort from the centre of the area to come back off the bar.
But that was as good as it got for the group favourites as Steaua held out for a valuable point.