Horner was given his marching orders by the energy drinks giant earlier this month following 20 years at the helm of the squad.
The Brit was reportedly given no reason for the sudden decision.
It came over a year after internal investigations into alleged inappropriate behaviour towards a female colleague were dismissed.
This year the team, which has lost key technical staff including designer Adrian Newey, has slipped behind McLaren in competitiveness.
That’s led to suggestions star driver Max Verstappen could want out at the end of the season.
Asked by Canadian broadcaster TSN if he was surprised by the Horner sacking, Brown said: “Maybe the timing, but not the result.
“I think there’s been a lot of drama there the last couple of years and it doesn’t seem like that drama has been calming down.
“Maybe it’s been getting worse. So, I’m not surprised.”
Ecclestone says Red Bull treated Horner ‘like he murdered somebody’
Horner is already being linked with a return to F1 elsewhere, although it is unclear how long he will remain bound to Red Bull.
“Given his age and his history in motor racing, I’d be surprised if he didn’t show up somewhere in motor racing,” said Brown.
“But I don’t know his other interests, whether he wants to go run a football team or what have you, so we’ll see.”
As for his interest in speculation surrounding Verstappen’s future, Brown added: “I couldn’t be happier with Oscar [Piastri] and Lando [Norris].
“So, short of being an interested spectator, I’m very happy with my driver line-up. I don’t really spend any time on it other than what pops up on my phone.”
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