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The Ibrox manager saw his side lose out again to their Old Firm rivals at Ibrox as Tom Rogic and Leigh Griffiths handed the Hoops a 2-0 win.
But Caixinha was furious Brown was allowed to remain on the pitch after his clash with Gers’ Colombian hitman just seconds before the interval.
He even had a nose-to-nose confontation with the Parkhead captain as the teams made their way down the tunnel and was still fuming over the incident after the full-time whistle.
“I was angry at half-time, did you see it?” asked Caixinha. “It’s the second time it happened, it was the same in April.
“I saw an elbow from Brown and I told the fourth official - but the referee let it go.
“Scott Brown was coming off and I told him, ‘You do that, but if I was on the pitch you wouldn’t’.
“I wouldn’t have allowed him to put his elbow in my face. If someone does nothing, I have to defend my club, my players and the truth of the game.
“It’s the referee’s decision. If he doesn’t think it’s an action to get booked or sent off, it’s his decision. I need to respect it.
“If I was a player and I had to face Brown or players like him, it would be a different thing. It was a shame that I couldn’t play because I know the mentality I have.”
Celtic boss Brendan Rodgers admitted he did not see the incident but praised referee Craig Thompson for his handling of the powder-keg clash.
“I thought it was a competitive game,” said the Northern Irishman. “It was aggressive and you want it aggressive.
“But I think we need to give a mention to the referee as well because he was excellent.”
Rodgers had every reason to be happy with his side’s work as they marked 500 days since their last domestic defeat.
They were pushed all the way during the opening half but when Tom Rogic swept the visitors ahead five minutes into the second period, their victory was set.
Griffiths then managed to slip away from Gers’ teenage debutant Ross McCroie for the first time all afternoon to slot home the second on 66 minutes as the Hoops once again underlined their dominance over their Old Firm rivals.
“I thought defensively we were outstanding in terms of our pressing and denying them the opportunity to play,” said Rodgers.
“In games here you have to defend well and have good organisation.
“In the second half, our conditioning and quality of our players came through. It was a very, very good performance. There was a great atmosphere here today and our boys coped with it well.”
Caixinha admitted Gers’ second-half errors and a stunning reflex save by Craig Gordon from Morelos’ point-blank range header in the moments after Rogic’s opener cost his side.
“The team who made the least mistakes won today,” said the Portuguese coach. “They were better than us as the game went on, definitely.
“We tried to take the game in the direction we wanted. In the first half, it was a good football match.
“But two moments were crucial. The first was how we lost the opening goal and the second was not equalising when Morelos had the chance.”
Celtic now hold an eight-point lead over their old foes but Caixinha has thrown down the gauntlet to his men.
He said: “We need to focus on the next match because now we’re going to see what we’re made of. Now we’ll see if we react the way we need to or just look around and don’t take decisions.”