The team suspended him for the game Tuesday against the Ottawa Senators (7:30 p.m. ET; BELL TV, MSG-B, RDS, TSN5, NHL.TV).
"There were some things this weekend that shouldn't have happened," Kane said Tuesday. "They won't be happening again. I can assure you guys of that.
"First and foremost I want to apologize to my teammates for letting them down. With what happened, me missing practice (Monday) was irresponsible and I take full accountability for my actions with what happened.
"It's something that should have never happened. It's something that I can promise you won't happen again and it's something I'm definitely going to learn from."
Kane said he had spoken with members of the organization, including coach Dan Bylsma and general manager Tim Murray, about the incident.
"Like I said, we are all on the same page moving forward," Kane said. "I'm happy with that and looking forward to putting this behind me and getting back on the ice."
Kane said Tuesday the missed practice should not be construed as a lack of dedication to the Sabres or the game of hockey.
"I think if you watch me play on the ice, I do take hockey seriously," Kane said. "I think I can take it more seriously. I think going forward you are going to see that out of myself."
Kane, 24, is fourth on the Sabres in goals with 16 behind Jack Eichel, Sam Reinhart and Ryan O'Reilly, who each have 17. He has been their hottest player lately with five goals in his past six games.
Kane said the most difficult part of the experience is not being able to help his teammates against the Senators.
"That was probably the hardest thing with everything that went on is I let them down," he said. "I'm obviously extremely disappointed in myself in not being able to go out there and battle with them tonight against Ottawa. For me, I addressed them yesterday as a group and I couldn't have asked for much more from them than the reception I got from them and just how supportive they were. For that, I can really thank them.
"It's something you obviously don't want to be in a situation where you have to [apologize], but it was absolutely necessary. I just wanted to be honest with them and apologize to them because I am sorry for the way things went down the other day. The last thing I want to be doing is sitting out, not playing and not being able to battle with those guys."
Sabres captain Brian Gionta said he was disappointed with what happened, but the players accepted Kane's apology and will help him move on.
"He apologized and that's where we will leave it," he said. "It was disappointing yesterday. The guys are there, guys are at practice and ready to work and you're missing one of your guys. It was disappointing for sure."
Gionta said the Sabres will miss Kane against the Senators.
"He's a big part of this team and he brings a lot to the table on the ice," he said. "For sure, it's disappointing and there are consequences for what happens. To be without him could hurt the team."
Sabres coach Dan Bylsma was asked if Kane was on a shorter leash after his absence from practice.
"He's on the same leash everybody else is," he said. "I think it's a concern he missed practice yesterday. It's a concern that he didn't show up and he's dealing with the consequences. We have rules and he broke those rules and he's going to deal with those consequences."
