The NHL announced the penalty Tuesday night.
Backstrom was facing an automatic suspension after he cross-checked Bruins forward Rich Peverley following the final buzzer of Boston's 4-3 victory Monday night.
Backstrom, who missed 40 games this season with a concussion, scored the game-winning goal for Washington in double overtime in Game 2.
"We disagree with the NHL's decision to suspend Nicklas Backstrom," the Capitals said in a statement Wednesday. "This has been a competitive and physical series, and we do not understand why a suspension was imposed in this case while other incidents in this series have not been reviewed."
After the Capitals held practice Wednesday morning, coach Dale Hunter said the Bruins are not playing only between the whistles.
"They were after the whistle and before the puck was dropped. They were doing stuff off the draw, like Milan Lucic going after Nicky's head," Hunter said. "We've got to play through it and let the refs do their job. We just have to play."
On Tuesday, before the suspension was announced, Hunter said Backstrom "was trying to protect his face," because Peverley had his stick raised. Hunter accused the Bruins of intentionally targeting Backstrom's head.
"It is crossing the line," Hunter said. "To grab his head all the time is not the right way to play."
Asked Tuesday, an off-day in the series, whether he believes the Bruins are targeting Backstrom's head, Hunter replied: "Oh, yeah."
"If you noticed it, every scrum, Nicky comes out with no helmet on. He gets blockered to the head by (goalie Tim) Thomas the game before," Hunter said. "So he's protecting his head."
Capitals forward Troy Brouwer echoed that assessment.
"There's been a couple times where they've gone after his head and grabbed him and thrown him to the ice," Brouwer said. "So I can understand why Nicky is a little bit nervous about when sticks come up."
Bruins coach Claude Julien did not appreciate Hunter's comments.
"It's ludicrous. It's ridiculous," Julien said Wednesday. "There's always going to be emotions in games and there are things that are happening. There were three cross checks and they penalized one and suspended one, but we're not whining about the referees and what's going on here. We need to win a game and we need to win a series. That's where our focus is on and that's where it should be."
Julien spoke at length about concussions and mentioned a tweet by Octagon hockey agent Allan Walsh, who wrote: "This has spiraled from out of control to total chaos. Do we really need a player to die on the ice for this insanity to stop?"
Walsh posted his tweet Tuesday night, likely after the Coyotes' Raffi Torres hit the Blackhawks' Marian Hossa during Game 3 of the Western Conference quarterfinal series. Torres has been suspended indefinitely until a hearing on Friday.
So far this postseason, there have been nine suspensions. There were only a total of seven during the entire Stanley Cup playoffs last season.
"I read something about an agent, Allan Walsh, that made a comment about that stuff, but they're the ones that are representing these players," Julien said. "These players are all part of the PA and the fact is, and I'll say it again, there's not a coach in this league -- not one -- that will tell his players to target somebody's head.
"Concussions are a serious and sensitive thing. We all respect that, so anyone who thinks otherwise is totally wrong."
Bruins center Patrice Bergeron, who nearly had his career ended in 2007 because of concussions, does not believe players headhunt in the NHL.
"No. Obviously, games are played hard, especially at this time of the year," he said. "I hope not."
The Bruins lead the series 2-1. Game 4 is Thursday in Washington; the best-of-seven series moves back to Boston Saturday for Game 5.
Information from ESPNBoston.com's Joe McDonald and The Associated Press contributed to this report.