The Germans were beaten 2-0 at home on Wednesday night, but their first-leg win in London three weeks ago saw them progress with the aggregate score 3-3.
"We have to look at this game in a very critical manner," Heynckes is quoted as saying by Sky Sports News.
"The early goal for Arsenal was obviously just what they were looking for. We had the better chances in this game, but lacked clinical finishing and weren't as calm as we usually are."
Bayern are back in Bundesliga action on Saturday, when they make the trip to Bayer Leverkusen.