The Dutchman squandered an opportunity to equalize from the spot against the German champions, and has said that he was sure that he would score.
The Bavarians were presented with a late chance to cancel out Robert Lewandowski's opening goal when the Dutchman was felled by Weidenfeller, only for the Dortmund keeper to save the resulting spot kick.
Citing his formidable record from penalties in recent times, Robben has now voiced his shock at missing the opportunity.
"This is a very bitter and disappointing defeat. In the end I don't know what to say," Robben began to Sky.
"I was so sure of myself. In the last three years, I think I've taken 10 or 11 penalties and converted them, but unfortunately I failed this time."
The former Real Madrid man went on to concede that Jurgen Klopp's side is the likely champion, but called upon his teammates to put the loss behind them as they pursue other targets.
"Dortmund have taken a huge step. We can almost say that Borussia Dortmund will be German champions," he admitted. "But we must now push on the throttle even more in the coming games."
Bayern Munich faces Mainz in the Bundesliga on Saturday, before locking horns at the with Real Madrid at the Allianz Arena in Champions League action on April 18.