The England international has been replaced by inexperienced John Flanagan, but the Reds boss said that he did not wish to alter his 3-5-2 system because of the absence of one player.
"You have a choice once you get the injury, change the structure of the side or bring a young player in," Rodgers told Sky Sports News.
"[Flanagan] hasn't had many chances, but his attitude has been second to none. Of course, quality is important, but it's also about having the right attitude.
"We only found out [Johnson] was injured today, we're disappointed he's got the illness as he travelled with the squad."
You can catch live commentary of this evening's game here.