Backstrom was given a match penalty for attempt to injure, which carried an automatic suspension. He will miss Game 4 on Thursday in Washington.
Capitals head coach Dale Hunter defended Backstrom's actions earlier Tuesday, saying he "was trying to protect his face," because Peverley had his stick raised. Hunter feels the Bruins are targetting the head of Backstrom, who missed 40 games near the end of the regular season with a head injury.
"It is crossing the line. To grab his head all the time is not the right way to play," said Hunter.