The Dutchman produced an assist and a dramatic, late deciding goal as Bayern defeated German rivals Borussia Dortmund 2-1 at Wembley on Saturday night.
And having missed a penalty in last season's final defeat by Chelsea at Bayern's own Allianz Arena after also losing the 2010 final to Inter Milan, the match-winning contribution was redemption for Robben.
After an enthralling game, he told Sky Sports: "There are so many emotions, especially where we came from last year and such a disappointment.
"The last four years, Bayern have been in the final three times. It needed to happen but you still have to do it."
He added: "It is a special feeling. You cannot describe it. Everything is going through your mind. It is hard to say but you do not want to be a loser."
Bayern could now complete an unprecedented Treble for a German club if they win their domestic cup final next weekend.
And Robben has been understandably impressed by a season in which they blew away Italian and Spanish champions Juventus and Barcelona en route to conquering Europe.
He said of the campaign: "It is already going into the history books. But also because of the way we did it. We beat Juventus twice 2-0 and then Barcelona 4-0 and 3-0."