Bayern had seemed to have qualification wrapped up after a 3-1 first leg win in London but the Gunners almost pulled off a miraculous comeback after winning 2-0 in Bavaria.
"I must say my players are leaving here with a black eye," said Heynckes. "I think I know European football, having had 150 games as coach in European Cups and I had warned my players.
"This was a timely reminder for us – that we have to continue working hard in order to achieve our goals.
"We failed to put up a real fight against them in the first half. We improved in the second half and created chances to score, but overall we never had real control of this match and were never able to pass the ball in the calm and controlled manner we are used to.
"This should be a reminder for us that it takes two games to qualify for the next round. We weren't as focused as we usually are. We weren't as compact or as aggressive as we have been in recent weeks."