The visitors raced into a 2-0 lead through Toni Kroos and Thomas Muller before Mario Mandzukic added a third after Lukas Podolski had temporarily given Arsenal hope.
Heynckes, who will leave Bayern at the end of the season, praised the quality of his charges and their ruthless punishment of errors committed by the Gunners.
"It was just easy for my team to play," Heynckes told reporters in his post-match press conference.
|AN IMPOSSIBLE TRIUMPH|
|150/1||Arsenal are 150/1 with Paddy Power to win the Champions League|
The 67-year-old was pleased with his team's devastating start to the match and keen not to underestimate the difficulty of winning away against a Premier League club.
"When you win in England against an English team, this is a huge success," he added to Sky Deutschland.
"We made a superb start with those two goals and we had a good game. Afterwards, our opponent showed that they are Champions League material."