The club suspended them for violating a team curfew Saturday night on the eve of Game 2.
General manager David Poile announced the scratches in a release.
"I've been a manager for 30 years, I care about each individual player, but I've never put an individual player above the team. In this case, the players violated a team rule," Poile told ESPN.com. "It's disappointing any time a player has to miss a game because of violating a team rule, and it's even more significant at playoff time, but the decision between the coach and myself was very easy.
"We have to do the right thing. Their actions spoke volumes in terms of their lack of commitment and focus to give our club a chance to win."
Radulov said the situation was between him and his GM.
"I'm going to get out there for our whole team, for all of the guys, and support and do what I can do for myself," he said. "Hopefully, those guys can get out there and win -- get Game 3. That whole situation -- I don't really want to get into it. I don't think it's good [to get into it]. Hopefully, everything is going to go well for our team and we'll battle through it."
Poile and coach Barry Trotz ran this decision by captain Shea Weber and other Preds' leaders before announcing it.
"We talked to the leadership group in terms of their knowledge of it and what have you," said Poile. "Everybody was very much aware of the situation. We had to do the right thing."
Defenseman Ryan Suter was part of the group appraised of the suspensions.
"We talked -- as a leadership group we talked with Trotz. We said whatever you decide, we will stand by you," Suter said. "We're in the playoffs, and we don't need distractions. Tomorrow we have to clear our minds and get back to play."
Both players were late-season additions, Kostitsyn coming over from Montreal at the trade deadline in late February and Radulov arriving in March after the NHL allowed him to leave the KHL in Russia and rejoin the Predators.
Weber, who played a behind-the-scenes role in bringing Radulov back to the NHL, supported the decision.
"Everyone needs to be held to the same standards and I think that's good," the captain said. "I think that everyone in here knows what the rules are and we're just going to move forward. We're focused on the game tomorrow. We dug ourselves a hole and we have to find a good way to get out of it."
Poile warned against overreaching conclusions because of this one incident.
"Let's not blow it out of proportion, it's not the first time a player has missed a game because of a team rule violation," he said. "We're full of second chances in this business."
The Predators trail their second-round series 2-0 to the Coyotes.
ESPN.com's Pierre LeBrun contributed to this report.