The Rams went on to nick the game 1-0 when Gary Teale netted with just five minutes of normal time remaining.
"Over the years he's been a real stalwart for us and that's why he's captain, but today he was petulant and unprofessional," City boss Johnsomn said after the match.
"He needed to keep his wits about him and not get involved in any petulance, but he did.
"He's apologised and he will do because he's a decent lad, but obviously he's let his team-mates down today and he knows that."
"I was disappointed that we weren't 1-0 up with the first attack, but I wouldn't take the victory away from Derby."