Jurgen Klopp's side - who finished runners-up to Bayern Munich last season in both Europe and the Bundesliga - were undone by Aaron Ramsey's close-range header at the Signal Iduna Park on Wednesday.
The result leaves Dortmund three points adrift of Group F leaders Arsenal and Napoli in second place, leaving a difficult task to ensure progression to the round of 16.
But Serbia international defender Subotic backed Dortmund to bounce back from the disappointing setback and reach the knockout phase by beating Napoli and Marseille in their remaining fixtures.
"This was a really, really important game for us," he said. "There are only six group games and we've now lost two of them.
"It would have been good at least to have picked up a point. We can rectify things, however, providing we win our next home game against Napoli.
"Then we'll have every chance of qualifying, it's still very open in the group."
Ramsey's goal came after a knockdown from Olivier Giroud left Subotic disappointed with the manner in which Dortmund conceded.
"The deep cross comes in towards Olivier Giroud, he nods it down, and it's left to Ramsey to poke it in from a few yards out.
"Everyone knows that with players like Bacary Sagna and Mesut Ozil, Arsenal are more than capable of whipping dangerous balls into the box, and that Giroud is very strong in the air.
"We were perhaps a little asleep, and had a reminder of exactly how good you have to be in the Champions League. Every mistake is punished."
