Keefe is being unnecessarily hostile here.
Kovacevic says they need to have a playoff mentality going down the stretch. Nothing wrong with that comment, the season is winding down and the Devils are in a playoff spot.
Keefe decides to use that opportunity to take a personal shot at Kovacevic's performance.
It can be somewhat justified (although still wrong) if Kovacevic said the team sucked, or the coach sucks, or made a negative comment about the team in which case Keefe's comment would basically be saying worry about yourself. But he didn't, he said the team needs to have a playoff mentality which is a generic comment that every player makes all the time and Keefe took it as a chance to criticize Kovacevic's play. Keefe clearly has issues with the player but there's no reason to bring it up to the media.
He could have just said Kovacevic is right and we need to play better. If he's still pissed at Kovacevic, go in the locker room and talk to him away from the cameras. The media feeds into this. Now they're going to be asking Kovacevic what he thinks about Keefe calling him out and he has to (hopefully) be the bigger man and put out the fire his coach unnecessarily started. If he responds with a shot back at Keefe, now this becomes an ongoing story until one of them leave the team or acts like the bigger man.