The Celtic captain was at the centre of three flashpoints as the Hoops defeated their rivals 2-1 on Sunday afternoon.
Alfredo Morelos was shown a first-half red card for an off-the-ball elbow on Brown. Ryan Kent then appeared to throw a punch at the midfielder after James Forrest had netted Celtic’s late winner.
After the full-time whistle Brown was involved in another incident as he was confronted by Andy Halliday following some celebrations in front of the Rangers support. Halliday was later shown a second yellow card for his part.
Gerrard said: “You’re playing against a player who loves to antagonise. Morelos and Kent are both provoked
“Celtic fans have the right to celebrate but to do it right in your race, Halliday has the right to protect his own people.
“The guy who antagonised it all from the beginning deserves to be punished as well. When you’re provoked, it’s only fair that both sides get punished in my view.
“We’ve hurt ourselves badly this season with a lack of discipline. I’ve given my players the benefit of the doubt on too many times. Morelos has asked me for a chat, and that will be picked up.”