Asham knocked out Beagle with two punches during a fight in the third period of Thursday's game, and as the Capitals forward lay on the ice, Asham made a sleeping gesture with his hands while skating toward the penalty box.
Beagle's faced was bloodied and he had to be helped off the ice.
"It's unfortunate the way the fight ended," Asham said after the game. "I obviously want to win but I don't want to go out there and hurt anyone. My gesture after it was done - I was into the game - it was uncalled for; classless on my part. I think those guys know I'm not that kind of guy to be going off, but it was a big game, I wanted to get my bench going, and classless move on my part."
The fight was Asham's 83rd in his career while it was just the first for Beagle. Capitals' captain Alex Ovechkin said that Asham was "not respectful" in fighting such an inexperienced player.
Earlier in the shift, Beagle caught the ire of Asham when got his glove up on defenceman Kris Letang, knocking his helmet off.
"I respect every guy that does that job, but that's bush league," NHL on TSN analyst Aaron Ward said of Asham's actions. "Your statement ends with a guy lying on the ice."
TSN hockey analyst Pierre LeBrun said that the league will not further discipline Asham, citing the fact he was remorseful after the game and didn't realize how badly hurt Beagle was at the time of the incident.
The Capitals won the game 3-2 in overtime.