Schaub picked up an ankle injury late in the third quarter and was replaced by TJ Yates, who went on to throw two interceptions including one that was returned 98 yards for a touchdown as the Texans fell to a 38-13 defeat.
The injury and Yates's subsequent introduction were cheered by sections of the home fans, something that Johnson believes showed "no class" on the supporters' part.
"It's bad when members of the other team are saying that's messed up that they would do something like that," Johnson told reporters.
"It just shows no class. It wasn't all the fans. But those are the same people that you're out somewhere with your family and you tell them they can't have an autograph right now, those are the same people that tell you you're rude.
"You don't cheer about nobody being injured - I don't care who it is. Guys lay their bodies on the line out there on that field. Some guys get injuries, and it affects them their whole lives. To cheer about something like that, it just shows they have no class."
The defeat was the Texans' fourth in a row as they fall to third in the AFC South with a 2-4 record.