Schaub, who became the first NFL player to throw interceptions that were returned for touchdowns in four consecutive games last week, was forced off with an ankle injury late in the third quarter of Houston's match against the St Louis Rams yesterday.
His departure was cheered by sections of the Texans fans, and Brown admits that he was speechless at the action of his side's own supporters.
"We appreciate you loyal fans and the fans that stick by us - I want to put that out there first. But for the fans that cheered when he got hurt, that's disgusting," Brown told reporters.
"You can feel how you want about him as a player, but this is his livelihood. This is how he provides for his family. When a man goes down and he's not able to get up and you're cheering, that's bad. It's all bad.
"You don't know what's wrong with him at that point. That could be the last play of his career. You don't know that. And for you to cheer and applaud that, I have no words for that."