Price got four minutes for roughing, but he could have been assessed a match penalty and ejected had the referee judged that he was using his blocker in an attempt to deliberately injure Palmieri.
That led to questions about whether the NHL would retroactively discipline Price.
Price lost his temper Thursday night after being bumped in his crease for the second time in one period. Price was bumped by Adam Henrique as the Devils center scored a goal, and then Palmieri slid into Price's knees, leading Price to jump on him and pound on his head and back.
"I got run over on the first goal and then I took another one and I got fired up, I guess," Price said.
Palmieri was dragged away as Price kept swinging and got a minor for goalie interference. The Devils forward called it "just a hockey play."
"I've done it probably 50 to 100 times in my career," Palmieri said. "You go to the net, and either it's a trip or a push or you lose an edge. It's going to the net. That's where you score goals. You go to the net, try to put a good shot on and you lose control.
"I don't know the rule, but any time you're on the ice defenseless and you're taking a blocker to the back of the head, it's not a great situation to be in."
The Associated Press contributed to this report.