The result meant the Germans dropped down to third in Group E and must now beat visiting Basel in their final game on December 11 to progress to the last 16.
Leaders Chelsea (nine points) qualified despite losing 1-0 at Basel on Tuesday. Steaua are bottom on three points ahead of their trip to London next month.
Chances were limited on a cold night at the National Arena in Bucharest and Schalke were decidedly lukewarm in attack.
Ralf Faehrmann, deputising for the injured Timo Hildebrand in goal for Schalke, was barely tested before the break but did well to parry a fine Federico Piovaccari volley on the half-hour.
Steaua needed to win to retain any chance of reaching the last 16.
The home team replaced ineffective midfielder Ionut Neagu with centre back Fernando Varela at half time and the home side began the second half brightly.
Steaua enjoyed more possession and Faehrmann had to produce an excellent save to deny Lukasz Szukala's effort 16 minutes after the interval.
At the other end Jermaine Jones missed the target with a firm header from a corner.
United States international Jones will miss the last match against Basel after being booked 15 minutes from time.
Steaua went close again in the closing stages through Cristian Tanase's delightful free kick and Nicolae Stanciu missed a good opportunity following a quick counter-attack.
(Reporting by Angel Krasimirov; editing by Tony Jimenez)
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