The 67-year-old has stated that the Gunners deservedly emerged victorious, and believes English football is not in crisis
The Bavarians only just managed to successfully defend their 3-1 lead from the first leg as they progressed on the away-goals rule, and Heynckes hopes they learnt from their mistakes.
"Arsenal scored two goals, but they didn't have more clear chances than that. Arsenal were better and dominated. We couldn't manage to dominate like we are used to doing," the Bayern coach said at the press conference.
"We will learn from this match. This may stop the euphoria from the people outside the club. They thought that Bayern were unbeatable."
Heynckes then went on to discuss the absence of any English teams in the quarter-finals of the competition.
"Some teams didn't make it so far and this time it's the English teams. But we have to admit that Manchester United had bad luck and Arsenal showed they are a top team.
"I think this doesn't mean too much. You have such periods in a country and I think the English teams will be successful again next year."