Berube replaced Mike Yeo, who was fired Monday after a 2-0 loss to the Los Angeles Kings.
"I thought our guys stayed with it," Berube said. "What I saw was they stayed with it and kept working."
WATCH: [All Blues vs. Predators highlights\]
Pekka Rinne made 28 saves for the Predators (16-5-1), who won their third in a row. Rinne passed Miikka Kiprusoff for the most NHL wins by a Finland-born goaltender with 320.
"A long time ago it wasn't even close to being on my mind," Rinne said. "[Kiprusoff] was well ahead of me and playing at a very high level when I was just trying to battle my way into the League. These are the things that you're not focused on, but it's pretty cool. When you're fortunate and stay in the League a long time you're going to face some milestones. This one, for sure, it's a cool one."