Heynckes’ side dominated possession and Bayern striker Mario Gómez squandered several chances to put the Bavarian outfit ahead, before Thomas Müller finally beat an impressive Petr Cech in the 84th minute.
But the Bundesliga side, who were looking to win the competition for the fifth time in front of their home crowd, conceded a late equaliser as Didier Drogba headed past Manuel Neuer.
Arjen Robben had a penalty saved by his former team-mate Cech in the first half of extra-time, and Heynckes’ men faltered in the shootout, allowing Drogba to score the winning spot-kick.
“Chelsea were the lucky team today; they played the way they know best and I’d like to congratulate them on their performance,” said Heynckes.
“They put on a real fight, defensively they were very well organised and in the shoot-out they had the luck to win the Champions League.
“It’s a very bitter defeat. We can’t blame Chelsea for playing their game. When you have so many opportunities you have to take advantage of them. We didn’t do that today and that’s why we lost.
“We must blame ourselves for having so many opportunities without profiting. When you score in the 83rd minute you need to keep that lead; then we had a penalty in extra time. Penalties are a lottery, we know that from history.”
The 67-year-old, who led Real Madrid to the Champions League crown in 1998, revealed his surprise that Bastian Schweinsteiger missed his penalty.
Heynckes also admitted that Bayern will take time to recover from the disappointment of squandering the chance to win Europe’s premier club competition for the first time in 11 years.
“These players had a huge fantasy about winning the Champions League here in Munich and then you have such a renowned, experienced player [Bastian Schweinsteiger] missing a penalty – that’s something you have to cope with,” he added.
“Bastian was instrumental in getting us to the final and he’ll take some time to get over it, but that’s football and you have to learn to cope with that.
“I said it would be something else to play in your own stadium, where you know everything and feel at home. The team played like we were at home, look at the statistics – we were better in every respect. The players delivered an outstanding performance and were not rewarded.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news