Chelsea, Robben's former club, went on to win the final in Munich on penalties after the midfielder missed a spot-kick in extra time.
The Dutchman said: "It was a terrible penalty kick. I wanted to shoot the ball hard and high in the goal but the ball didn't go high enough.
"I can't describe how I feel with words but it's been a terrible night."
In April, Arjen Robben also missed a penalty in Bayern Munich's 1-0 defeat in the Bundesliga against Borussia Dortmund, which was a crucial match in the title race.
Robben had his chance from the spot when Didier Drogba fouled Franck Ribery inside the box, but Petr Cech saved his kick.
He was consoled by Drogba and Uefa president Michel Platini after Bayern's 4-3 shootout defeat after the game had finished 1-1 draw after extra time.
"The fact that Drogba and Platini tried to cheer me up was nice, but it's worth nothing," Robben said. "I wanted that cup but it didn't happen."
Bayern manager Jupp Heynckes backed Robben for not taking one of his side's five spot-kicks in the shoot-out.
"You can understand if he didn't score the penalty in extra-time that he may have lost some self-confidence to participate in the penalty shoot-out," added Heynckes.
"That is quite easy to see."
Robben added: "After that, I still played well but you have to change your mindset at that point."
Bayern Munich's Arjen Robben admitted his missed penalty in the Champions League final was "terrible".