Bayern gained a measure of revenge for Tuesday's DFB-Pokal elimination at the hands of Freiburg when Matthijs De Ligt's stunning second half strike secured all three points at the Europa-Park Stadion.
The win saw Bayern Munich maintain their two-point lead over Borussia Dortmund at the top of the Bundesliga table.
Kimmich earned a yellow card at full time for clenching both fists and gesturing towards the home fans as a mass confrontation ensued for his actions.
The Germany international later accepted his behaviour was out of order.
"There were many emotions involved," he told reporters. "It was an important win for us – the DFB-Pokal defeat hurt deeply.
"I got carried away; I shouldn't be doing that. You can say it was unsportsmanlike."
Asked what provoked his actions, Kimmich added: "During the warm-up, there was a 10-minute film about the Pokal game being shown [on the big screen].
"I can understand anyone who describes [my reaction] as unsportsmanlike. In the end it's just emotions."
