The Ivory Coast international praised his side's refusal to give up and singled out the performance of goalkeeper Petr Cech as key to the Blues' victory
The Blues secured a famous 4-3 victory on penalties at their opponents' home ground after taking the game to extra-time thanks to Drogba's late equaliser.
The Ivorian also coolly slotted home the all-important final penalty to secure the win for his side, after Bastian Schweinsteiger's miss handed the Blues the advantage.
Drogba told ITV: "[Chelsea] never give up until the end. This team is amazing. It was written, I think, a long time ago.
"I want to dedicate this cup to all the managers we've had before, all the players I've played with before."
Drogba also hailed the performance of goalkeeper Petr Cech, who saved a penalty from Arjen Robben in extra-time before playing a key part as Bayern missed twice in the shoot-out.
"When we have this guy in goal you have to believe," he added.