Lampard hit one of Chelsea's four successful penalties and the 33-year-old, who joined from West Ham in 2001 and captained them tonight [Saturday] in John Terry's absence, savoured the club's glory night.
He said: "I can't believe it. The determination we've shown... we didn't play fantastic but the main man Didier dug us out of trouble there.
"He's a hero. Without him we're not here.
"He scores the goals in the big games."
Lampard said of Drogba, who is out of contract this summer: "I'd love him to stay. What he did tonight [Saturday] he's been doing all his career."
Of the club's triumph, Lampard said: "It means everything.
"We've been so many years trying to do this.
"This is the one we really wanted and we've got it."
Asked whether the win should lead to interim manager Roberto Di Matteo being given the job permanently, Lampard said: "It's not a question for this moment.
"He took us from a struggling team maybe going out of the Champions League and we won it, so look at that."
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Ashley Cole, who scored one of his side's penalties in the shoot-out, admits Chelsea rode their luck in the final as Bayern spurned a number of good chances but felt they were deserving winners in the end.
He said on Sky Sports 1: "I'm lost for words. We should have probably lost the game with the amount of chances they had.
"We rode our luck, you need luck in this competition if you're going to win it. Today [Saturday] we rode our luck but we deserved it today."
Asked if he thought their luck might have run out when Bayern won a penalty five minutes into extra-time, the England international added: "Not really, with the players we've got here we thought, 'ok it's a penalty but we still have time had time left', and when Petr's making great saves like that we always believe."
The victory means it was third time lucky for Cole in the Champions League final having been on the losing side with Arsenal in 2006 and Chelsea in 2008.
The 31-year-old said: "This is the reason I came here."
Absent skipper Terry still got to lift the trophy, sharing the duties with Lampard, and afterwards he called for Di Matteo to be given the job on a full-time basis.
"Robbie has been fantastic since he came in," he told ITV 1.
"You look at that trophy. That's certainly what we've been waiting for, what the owner's been waiting for, what the owner was in tears for.
"He's strived for this, he's pumped an awful lot of money into this football club trying top achieve that. Tonight [Saturday] we've done that and Robbie deserves a lot of credit for that."
On the Italian's chances of becoming manager permanently, he added: "We hope so. He's been fantastic. He can't do any more than he's done. To win the FA Cup and the Champions League, he can't do more than that."
The England international also added on Sky Sports 1, that he was grateful to UEFA for allowing him to carry the cup.
"It means the world to me," he said.
"It was a great touch from Frank and a really nice gesture from UEFA.
"It was a really unfortunate situation I put myself in, but on nights like this you have to be involved."