While Hazard is likely to receive a three-match ban for violent conduct, Morgan became an overnight Twitter sensation, gaining 100,000 followers in 48 hours.
Rodgers, who managed Swansea for two years before moving to Anfield joked: "I know Charlie well. He used to do it great for me! He was taught well!
"He is a good boy is the kid. He loves his club and he loves his football."
He added: "Don't get me wrong, ball boys are well tuned in to what is required in the game. There was maybe a wee bit of gamesmanship by Charlie but certainly nothing sinister.
"He is a real good kid who loves his football club. I think any manager, player, coach would be happy if their ball boy did that."