Prust said Watson "kept provoking" him and insulted him during Sunday's game, adding that the referee "tries to play God." It's unclear what, if any, discipline Prust may face from the NHL.
"I'm old school with those things," Therrien said on a conference call Monday. "I'm a true believer that what's in the dressing room should stay in the dressing room, what's on the ice and comments should stay on the ice. And we'll take care of that internally."
Therrien said he had not heard from the league regarding Prust's comments. Under the terms of the collective bargaining agreement, Prust can not be suspended.
Prust could, however, be fined. The NHL docked Alexandre Burrows of the Vancouver Canucks US$2,500 in 2010 for detrimental comments about referee Stephane Auger.
Therrien did not seem concerned about Prust's comments having a negative effect on the rest of his team's series against the Tampa Bay Lightning.
"We all understand they have a difficult job, it's not always easy for referees," Therrien said. "They try their best. What happened yesterday, it happened yesterday, and my only concern is on our next game."
The Canadiens trail the Lightning two games to none. Prust racked up 31 penalty minutes in a 6-2 loss at Bell Centre, including a 10-minute misconduct and a game misconduct after tripping goaltender Ben Bishop and fighting Braydon Coburn.
Tampa Bay centre Brian Boyle, a teammate of Prust's with the New York Rangers, was surprised at the antics near the end of the game Sunday.
"I didn't see a lot of that when we played together," Boyle said on a conference call. "That was out of the ordinary, I think, last night from what I saw with him."
Coburn was the closest opposing player to Prust and Watson but said he didn't hear their interaction. The Lightning defenceman didn't want to comment on the specific incident but said he was surprised to read Prust's comments and understands emotions run high in the playoffs.
"I know in the past (with) referees, they give you a stern warning and it's usually in your and your team's advantage to listen to them because obviously they control the game out there in terms of calling penalties," Coburn said.
Follow @SWhyno on Twitter