Johnson, who signed a five-year, $16.25 million deal with the Penguins, said Sunday, "I've been looking to be in a winning culture."
Reached by The Athletic for reaction to Johnson's apparent slight, Tortorella said, "All I know is this organization, from the lawyers, the front office, J.D. [John Davidson], the managers, the coaches, players ... has done nothing but try to help Jack. And for him to backhand slap us like this is utter bulls---, and he should know better.
"No one wishes anything bad to happen to him and his family. We wish him the best. But for him to put it the way he put it today is bulls---. And to have a general manager question our decision-making from three hours away, he must be a f---ing magician."
Tortorella's latter comment referenced Penguins GM Jim Rutherford, who said of Johnson, "I don't think he had a bad year. He was a healthy scratch at the end of the season. I know the reason why. It wasn't because of how he was playing."
Blue Jackets GM Jarmo Kekalainen, according to The Athletic, said he would be calling Rutherford for an explanation of that comment.
"The thing that pisses me off the most is a general manager in this league questioning and talking about our decision-making," Tortorella said.
"Jack and I had an open, honest conversation all through this. Jack and I have known one another forever, and I love the guy. There's no agenda here. You think that's an easy decision for me, after what Jack Johnson has been in this league and what he is?
"But that can't get in my way as far as making the right decisions for this hockey club, and that's all we do, so Rutherford should shut the f--- up."
Johnson, 31, a 12-year veteran who had three goals and eight assists in 77 games last season in Columbus, later told The Athletic that his comment was not meant to criticize his former club.
Johnson said he misspoke at his news conference and he never meant to disparage the Blue Jackets' organization.
"I didn't mean it in any way, shape or form as a backhand towards Columbus," Johnson said. "Pittsburgh's won two [Stanley] Cups in the last three years, and there's a winning culture there. I didn't mean it in any way to insult the Blue Jackets at all."