Halliday was one of two Rangers players to be sent off for incidents involving Brown.
After just half an hour, striker Alfredo Morelos elbowed the Celtic captain in the face off the ball in response to apparently being goaded.
Then, after the game ended, Brown ran over to celebrate in front of the travelling Rangers fans, in a move which incensed Rangers players.
At this point, Halliday squared up to the midfielder and started a mass brawl.
The win effectively ensures that Celtic will win their eighth straight Scottish Premiership title this season, as they are now 13 points clear at the top of the table.
Speaking after the game, Gerrard admitted that he felt bad for Halliday and admitted that he would have done the same thing.
”I feel for Andy,” he said.
“Celtic are well within their rights to celebrate, they’ve won the game and they’ve stretched their lead.
“We celebrated when we won the last Old Firm game, so you are well within your rights.
“But I can’t understand why a guy (Brown) then decides to celebrate 10 yards away from the two per cent of Rangers fans when they’re 98 per-cent home support.
“Andy went in to protect his own people – I would have probably done that myself.”
Gerrard was less lenient on Morelos, however, and promised to fine the star.
Sunday’s red card was his fifth of the league season, and his fine will be redistributed to Rangers fans.
“I’ve gone above and beyond for Alfredo,” Gerrard continued.
“I’ll continue to protect him, support him and love him, because of the player and the person he is.
“But I’ve got to draw a line. He’ll be punished. I’ll recommend to the board he’s fined a week’s wages –and that the money should go to the supporters who came today.”
Liverpool loanee Ryan Kent was lucky to avoid a red card after punching Brown in the face after Celtic’s winning goal.