Bayern were presented with their first trophy in three years at the conclusion of their penultimate league match of the season, having clinched the title weeks ago.
"No team in the history of the Bundesliga have ever played football the way we have this year," said Heynckes, who will be replaced by Pep Guardiola at the end of the season.
"We played at a consistently high level and that fills me with pride."
As he took to the balcony of Munich's City Hall to greet an estimated 20,000 fans, Heynckes saw what the title meant to a club without a major success since their league and cup double of 2010.
"Your excitement tells me that you were starved and that you've been waiting for what feels like a decade to be back here," he told supporters.
"We'll now do all we can to ensure we get what we are all dreaming about on May 25."
May 25 is the date of the Champions League final, when Bayern will hope to complete the second part of their treble bid with victory over Bundesliga rivals Borussia Dortmund at Wembley.
A week later, on June 1, Heynckes' last match at the Bayern helm will come against Stuttgart in the final of the DFB-Pokal.
"We've not finished yet," added Bayern captain Philipp Lahm. "We want two more titles."
Reflecting on yesterday's title celebrations, Lahm said: "It's a dream to see how many people are here. It's sensational.
"This trophy is back in Munich, where it belongs."