Clarke included 16-year-old Academy product Brown on the bench for only the second time on Saturday.
But he insisted the way the game went in the 2-1 defeat by Arsenal meant there was no opportunity to hand him a top-flight debut.
"I think the type of game that evolved meant it wasn't the type of game to bring him in," he told the WBA website.
"Don't forget he's not even 16 and a half yet. He's a very young 16, and is just out of nappies to be honest.
"But it's good to keep him involved. He trained last week and he was excellent and deserved his spot on the bench.
It's a great experience for him and being 16 he'll enjoy days like that."