Werenski, a 22-year-old defenseman, is a restricted free agent. The Blue Jackets open training camp Sept. 12.
"I'd be terribly disappointed," Tortorella said in comments published Tuesday. "I'm not involved in the business part of it. But for a young man to miss one minute of camp … it disgusts me. That guy there, Werenski, the way he has evolved here. He has shown so much determination, so much more confidence and attention to detail playing defense without it really affecting his offensive game. He has really grown as a player. I just don't want him to miss a beat here. I won't be disappointed, I'll be disgusted."
Werenski had 44 points (11 goals, 33 assists) in 82 games last season. He had six points (one goal, five assists) in 10 Stanley Cup Playoff games.
Selected by the Blue Jackets with the No. 8 pick of the 2015 NHL Draft, Werenski averaged 22:54 of ice time last season. He has 128 points (38 goals, 90 assists) in 237 NHL games.
"I thought he started becoming a man last season," Tortorella said. "He's still up the ice and he's still making plays, but his determination on pucks, his determination of playing in those areas, not allowing people to get to the net on him, it improved tremendously. I thought he was soft a year ago, but then he really came on."
Tortorella also discussed the departures in free agency of forwards Artemi Panarin (New York Rangers) and Matt Duchene (Nashville Predators), and goalie Sergei Bobrovsky (Florida Panthers), and wondered if his coaching style had a role in their decisions to leave Columbus.
"Maybe they don't like playing for me," he said. "That's fine. To me, eventually, you're not playing for the coach, you're playing for your teammates, and that's where I saw the camaraderie and the arrogance … I could see all of that building. I guess I feel like the players. I think the players respect them, respect the rights they had to do what they did. But I'm [angry] too, just like the players. I'm saying, '[Heck] with them, we want to be here, let's get it together and get going.' I wish them nothing but the best, but I'm [angry] that they leave Columbus, because I think we've got a really good thing going here."
Bobrovsky, who won the Vezina Trophy twice in his seven seasons with the Blue Jackets, leaves the largest hole. Joonas Korpisalo, Bobrovsky's backup most of the past four seasons, could be the starter, with 25-year-old Elvis Merzlikins, who played the past six seasons in Switzerland, competing for ice time.
"I want to see where we're at with those guys," Tortorella said. "Even though (Korpisalo) has been here, he still hasn't been the No. 1 guy. It'll be him and Merzlikins, I believe. But the shadow of Bob not being there is big. When Bob was struggling, Korpi would come in. When Bob needed a break, Korpi would come in. Well, now Bob is gone. It's right there for Korpi, but it's totally different when the No. 1 guy isn't there. Now you have to go win a job."