Hazard was dismissed by referee Chris Foy after losing patience during the closing stages of the League Cup semi-final second leg at the Liberty Stadium, when Morgan refused to hand over the ball after it had gone out for a goal kick.
Morgan, 17, fell to the ground as Hazard attempted to get the ball from him, with the Blues player then trying to kick it from under him but appearing to instead make contact with the youngster.
Morgan and his father, Swansea's largest shareholder Martin, decided not to press charges following the incident, although South Wales Police are following up complaints from members of the public in Sussex, Kent and south Wales.
Hazard and the ballboy also apologised to each other in the Chelsea dressing room after the final whistle.
The Football Association said it was continuing to review footage of the incident and the Belgian's automatic three-match ban for violent conduct can be increased in "exceptional circumstances".
Swansea will not face any action over Morgan's role in the incident, as any complaint of time-wasting is considered an issue to be handled by the officials during the game.
Swansea stated after the game they had not told their ballboys to delay giving the ball back to the players, although Morgan had used the words "needed for time-wasting" in a post on his Twitter account - which has rapidly acquired some 90,000 followers - a few hours before kick-off.
It is not the first time Hazard's frustrations have got the better of him - in 2011 he stormed out of the stadium after being substituted during a Euro 2012 qualifier for Belgium and was filmed tucking into a burger from a van outside.
And Steven Martens, the chief executive of the Belgian FA (KBVB) said: "It's unfortunate and of course it's not something we are proud of.
"No football authority or person interested in football likes to see acts of violence or lack of respect and this is what happened.
"It might have happened in the heat of the fire but professionals are expected to be able to control themselves.
"They have to be able to control their emotions and when they don't that's unpleasant in general.
"Of course, as we are the Belgium FA we don't like it to be a Belgium national squad player but I am very much convinced that Eden himself will realise that.
"Eden is more than intelligent enough to understand that this is going to be a lesson learned.
"All of us make mistakes in life."
Professional Footballers' Association chief executive Gordon Taylor does not believe Hazard should face an FA charge over the unsavoury episode.
He said: "There is obviously a process which the FA have to go through and it is up to them what they decide.
"But I don't think the young lad involved would want to see Hazard punished further."