The Serbia international was involved in the build-up for Marco Reus' 91st-minute equalizer that made it 2-2, before Felipe Santana secured a famous win at Westfalenstadion with a close-range finish two minutes later. Santana's goal was necessary or else Malaga would have gone through on away goals.
"Up until now, our story has been like a Hollywood movie - hopefully it will have a Hollywood ending," Subotic told UEFA after the final whistle.
Malaga had gone 1-0 up in the first half through Joaquin, before Dortmund leveled thanks to a fine team move that was finished by Robert Lewandowski. The Liga side retook the lead through Eliseu with eight minutes remaining on a controversial goal with the scorer appearing to be in an offside position, but eventually lost out to two late strikes.
"I just can't really believe it," Subotic added. "This is the craziest moment in all of my footballing career.
"It has been a special match for everbody - for us and the fans."
Dortmund CEO Hans-Joachim Watzke echoed Subotic's shock at the club's late victory.
"I've never experienced anything like it," Watzke told Sky Sports. "It is the most emotional moment you can have. It is hard to realize, maybe in a few days we will.
"One moment you're dead and in the next moment you're in the semifinal. It is crazy.