Karl, 18, put the German champions ahead just before half-time and celebrated by putting his finger to his lips in a "shush" gesture towards the home fans, who took it as a provocation and booed the winger for the remainder of the match.
Harry Kane went on to secure a 2-1 victory for Bayern, but Karl felt the need to clarify his celebration afterwards.
"It's the emotions that take over. I'm sorry if the fans misunderstood me, that wasn't the intention," Karl said.
"Most football fans know it's about emotions, and that it's simply part of the game. I'm sorry about that."
Elversberg, freshly promoted to the Bundesliga, had hoped to cause a major upset against the visitors, and while the shock did not materialise, the home side put in an impressive display and came close to taking a point off the champions in front of their own fans.
Midfielder Maximilian Rohr was pleased with his side's performance despite the defeat.
"We might have lost, but I'm so happy to have played against a team like that," Rohr told Bayern Munich's official website. "I think we did well, and we can be proud of our performance."
Elversberg have made a solid start to life in the Bundesliga, sitting on six points from three matches following their promotion, and next travel to face Schalke 04 in their upcoming league fixture as they look to build on an encouraging start.