The Dutchman squandered an opportunity to equalise from the spot against Jurgen Klopp's men, and believes the Bavarians have blown their chance of domestic glory
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 miss allowed Borussia Dortmund to become the first team to beat Bayern Munich in four consecutive Bundesliga matches since Otto Rehhagel's Werder Bremen managed to do so between 1991 and 1993.
The former Real Madrid man conceded that Jurgen Klopp's side are now the likely champions, but called upon his team-mates 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 face 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.