Dortmund head into the second leg of their quarter-final with a 3-0 deficit, having been comprehensively beaten by Real at the Bernabeu.
Jurgen Klopp's men - beaten Champions League finalists last term - would appear to have little hope of progressing.
Forward Reus, who scored the winning goal against Dieter Hecking's men, still harbours ambitions of reaching the last four of Europe's premier club competition.
"We have not given up," Reus told Dortmund's official website. "If we play like we did (against Wolfsburg) in the first half, then it becomes very difficult.
"If we play as well as we did in the second, it may even work out. It is damn hard, (but) we'll give everything. In football, everything is possible."
The former Borussia Monchengladbach man dismissed suggestions that he had intentionally handled when controlling the ball following Grun's mistake.
"How am I able to move my hand away so fast? Even if I had not affected the ball with my hand, I would probably nevertheless have scored the goal," Reus added.
"From there it - as I already said - was a perfectly good goal."
