Bayern had the upper hand for most of the 1-1 draw at their own Allianz Arena but wasted a bagful of chances and an extra-time penalty before the English club snatched the top European club trophy in the penalty shootout.
"This was not about who won in the penalties," Heynckes said. "This was about us not using our chances to win the game. It is purely our fault that we did not use our many chances.
"My team played an outstanding game against an opponent who played as we expected them to do," said the 67-year-old coach, who won the title with Real Madrid in 1998.
This was the second consecutive season that Bayern were left without any trophies.
They had though looked on track for their first Champions League victory since 2001 when Thomas Mueller headed in for a much-deserved lead in the 83rd minute after the Bavarians played cat and mouse with a defensive Chelsea for much of the game.
"It is difficult to put what we feel into words," a dejected Mueller said. "This is football and we have seen it so many times in the past that it is not always the team that deserves it that holds up the trophy in the end."
Bayern then conceded an 88th-minute equaliser through Didier Drogba, who later brought down Franck Ribery in the first half of extra time for a penalty.
But instead of firing the Bavarians back into the lead, Robben saw his spot kick saved by keeper Petr Cech before the Dutchman refused to take a penalty in the shootout.
"If you see the game we played tonight you would have never thought that Chelsea would walk away as the winners."
"We just could not figure out how to convert our many opportunities. You have to score because if you don't you will be punished," Heynckes added.
Bayern president Uli Hoeness was equally baffled.
"I have absolutely no explanation as to why we lost," he said. "We scored our goal at a great moment, then we get a penalty and have a superb chance through Olic and then we still can't do it.
"If you have that many chances you have to seal the deal."