In snowy conditions inside the Arena Nationala, the German side thought they had edged in front when Christian Fuchs turned Jefferson Farfan's cross into the net, but the referee adjudged that the ball had crossed the dead-ball line before the cross came in.
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Schalke thought they had earned a penalty after the break when Farfan's ball into the box fell into the path of Benedikt Howedes who fell under the challenge of Iasmin Latovlevici, but the referee turned down his appeal.
Steaua had their own penalty shout turned down when keeper Ralf Fahrmann attempted punch appeared to connect with Federico Piovaccari instead of the ball, but in the end both sides had to settle for a point.
Despite the draw, Schalke can still qualify for the knockout stages if they beat Basel in their final group game in Gelsenkirchen next month.