The incident happened during the Blackhawks' preseason opener Wednesday in Winnipeg.
"It was just stupid," Boynton said. "I was upset. He beat me up, whatever. It was a stupid play on my part and I'm paying for it.
"It sucks, but I made my bed, now I have to sleep in it. It's unfortunate, but that stuff happens."
Boynton will miss Chicago's regular-season opener against the Colorado Avalanche on Oct. 7.
The suspension cost him $2,688.17, with the money going to the Players' Emergency Assistance Fund.
"I've been around," Boynton said. "I know better. It hurts the team, keeps me out a game, and it looks bad for the organization. I've apologized to who I have to apologize to ... and it won't happen again."
The NHL had sent out a video to all of the teams illustrating behavior that wouldn't be tolerated, and the throat-slash gesture was included.
Jesse Rogers covers the Blackhawks for ESPN 1000 and ESPNChicago.com.