Bettman spoke Tuesday after vice president of player safety Brendan Shanahan gave his address on the final day of the Board of Governors meeting.
Shanahan handed out a two-game suspension earlier in the day to Toronto captain Dion Phaneuf for his hit from behind on Kevan Miller of the Boston Bruins.
Shanahan gave Pittsburgh forward James Neal a five-game suspension earlier in the week for kneeing Boston forward Brad Marchand and scheduled an in-person hearing for later this week with Bruins forward Shawn Thornton for grabbing Pittsburgh defenseman Brooks Orpik from behind, throwing him to the ice and punching him.
Bettman said the league has been proactive about eliminating dangerous hits to the head, and only about 50-100 of the approximately 55,000 hits in a season are problematic.
"I believe the sense of the room is that Brendan Shanahan and the department of player safety has the confidence of the board of governors. He certainly has my confidence," Bettman said. "It's about modifying an element of the game's culture and we think we've made positive, dramatic steps forward."
In other topics, Bettman said there are no current plans for expansion despite interest from various markets. Seattle, Quebec City and Ontario are among the markets believed to have interest in adding a team.
The recent realignment has eight teams in each division in the Eastern Conference and seven teams in each Western Conference division. There could be interest in adding two franchises to leave all four divisions with eight teams.
Bettman also said the league will wait until the Olympics in February before deciding whether to keep participating for the 2018 Winter Games in South Korea. He also said the league and union have had discussions about bringing back the World Cup of Hockey.