Los Blancos were routed 4-1 in Wednesday night's first leg at Signal Iduna Park, with Robert Lewandowski scoring all of the home side's goals, and will need to perform quite the comeback next week at Estadio Santiago Bernabeu to progress.
Madrid now faces a monumental challenge in trying to keep its hopes of a 10th European Cup success alive, but Casillas still believes his club can do it, provided both the club's players and supporters are ready to give their all for the cause.
"I ask for the public's help," he told reporters on Thursday. "Tuesday will be the most important game of the season.
"To lose 4-1 in the semifinal of the Champions League is always painful, but the locker room is already fired up by the knowledge that there is still a second leg to play.
"We have to fully understand the situation, as should our fans. They must understand how important this game is and how important it is for them to be heard.
"It's even more important than the derby in the next round of the championship. We must die on the field, because there is a final at Wembley at stake."
Some Madrid fans, of course, might be alarmed by Casillas' comments on Saturday's trip to Estadio Vicente Calderon, but the currently benched Blancos skipper is adamant that the return leg against Dortmund takes precedence.
"Of course, the derby is important," the Spain international acknowledged. "Atletico have not won one for 14 years, but against Dortmund, I repeat, it's the most important match of the season."
Meanwhile, even though Casillas is currently kicking his heels on the sidelines, he insists that there has been no falling out with Blancos boss Jose Mourinho.
"From the professional point of view, there is a lot of respect for Mourinho," Casillas said. "And like Xabi Alonso has said, the team comes first."
"I am continuing to help the team, from the dressing room. I help in a different way, but I am there and I am training as usual."
Madrid must win Saturday's derby with Atletico if it is to ensure that Barcelona will have to wait another weekend to clinch the Liga title.