Klopp said Friend's performance during the 1-1 draw with West Ham was affected by the decision to allow Liverpool's goal.
"I heard our goal was offside. I'm pretty sure the ref knew it," he said.
According to the FA Klopp was charged as the comments made "questioned the integrity of the referee and/or implied bias".
Klopp said Friend, referee, "did not want to open the gap any more" in the second period following his error.