The Bundesliga side were comprehensively beaten at the Bernabeu, but despite his side's slim chances, Reus believes that there is still an opportunity to go through.
Dortmund were given a confidence boost with the 2-1 comeback win over Wolfsburg on Saturday, and Reus has urged his team to replicate their second-half performance against Real.
"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."
Reus joined Dortmund from Borussia Monchengladbach in 2012.