The Blues triumphed at Bayern's home ground, coming from behind to level the match with a Drogba header, then overcoming the Bavarians on penalties.
And writing in Commitment, his new autobiography, the Ivorian revealed the techniques that he used to try and make sure Robben missed his crucial penalty.
Along with Lampard, Drogba tried to remind the Dutch forward of his Chelsea past, suggesting goalkeeper Petr Cech would know where he wanted to place the spot-kick.
"Arjen, you're a Chelsea player, you can't do this! Don't do it! Anyway, we'll know where you're going to shoot," Drogba and Lampard said to Robben, according the Ivorian's autobiography.
"We got inside his head, definitely, because his kick was weak – definitely weaker than it would normally have been – and Petr saved it," Drogba suggested.
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The Montreal Impact player believes that his tactics had the required effect, as Robben missed and Chelsea went on to win the Champions League.
That win marked Chelsea's first Champions League triumph, coming after a remarkable semi-final victory over favourites Barcelona, with the Blues hanging onto their result late in the game.
Roberto di Matteo was charged with guiding the club through the latter stages of the European campaign, but Drogba revealed that the players made their own tactical decisions, with Jose Bosingwa overrriding the manager's orders in the semi-final with Barcelona.
"The players really stepped up to take responsibility," Drogba writes.
"The manager was telling Branislav Ivanovic to play centre back but Jose Bosingwa said, 'No, no, I will play centre back', and carried on to say where he thought others should play.
"I remember saying. 'I can play left back if necessary. We don't need a striker. I'll play striker and left back, whatever it takes'."