Hanzal received a five-minute major and was ejected from the game for the hit on Brown in the third period of an eventual 4-0 Kings victory.
Brown was slow to get up after the hit but finished the game.
"I chip it by (Derek) Morris. I see (Keith) Yandle coming for the puck," Brown said after the game Tuesday. "I know there's a guy behind me, but I didn't think he was going to hit me. Because he probably saw my numbers (on the back of his uniform) from the top of the faceoff circle. He was behind me the whole way. It wasn't like I turned or anything. I was going to get the puck. I thought Yandle and I were going to have a puck battle, and then ... I mean, Hanzal's a big boy."
Coyotes general manager Don Maloney declined comment when reached by ESPN.com.
Brendan Shanahan, the league's head disciplinarian, said in a video released by the NHL that Hanzal violated Rule 41.1, which states, "A boarding penalty shall be imposed on any player who checks or pushes a defenseless opponent in such a manner that causes the opponent to hit or impact the boards violently or dangerously."
"Brown does not significantly turn his body just prior to, or simultaneously with contact," Shanahan stated. "He also does not suddenly change direction in a manner that contributed to the dangerous nature of this forceful hit from behind. Furthermore, after chipping the puck from the blue line, Brown does not possess, or even touch it again."
Shanahan went on to say there are some circumstances when a player contributes to a boarding penalty by leaving himself in an awkward position or while trying to "reverse hit" an opponent. Brown did neither in this case.
"Hanzal is directly behind Brown and his vision is focused on Brown," Shanhan said. "Hanzal then recklessly initiates the check from behind into the boards. He does not avoid contact and does not attempt to minimize."
Brown lay on the ice for several seconds after the play but eventually returned to the game. That played a part in determining Hanzal's punishment, as well as his clean history with the league, Shanahan said.
The Kings lead the best-of-seven series 2-0 and Game 3 is Thursday night in Los Angeles.
Information from ESPN.com's Pierre LeBrun, ESPNLosAngeles.com's Dan Arritt and The Associated Press contributed to this report.