The Boquerones were 2-1 up after 90 minutes of play and appeared to be on their way to the semi-finals of European club football's elite competition.
However, Marco Reus then restored parity before Felipe Santana's offside-goal well into stoppage time eventually saw Dortmund progress to the next round.
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"We are outraged because we are again the victim of injustice. We will file an official complaint to Uefa over the referee," Casado told reporters.
"It's a shame that in the quarter-finals of the Champions League the referee is not of the level that the players and the fans deserve, both from Malaga and Borussia Dortmund.
"Our complaint will be aimed at the referees rather than at Uefa. The Champions League is an elite competition and the people in it should be elite level, too."
Meanwhile, Malaga winger Joaquin, who netted the opener on Tuesday, even went as far as to claim Uefa deliberately favoured Dortmund.
"We suspect [Uefa president] Michel Platini and everybody else at Uefa wanted us out. It's much easier to do this to Malaga than to Real Madrid. This only happens to small clubs like Malaga..."
Aside from Santana's offside-goal, the match officials also failed to spot Eliseu was in an offside position when he scored to make it 2-1, while Dortmund defender Marcel Schmelzer escaped a red card after seemingly punching an opponent.