The Chelsea midfielder faces an automatic three-game ban after being dismissed for violent conduct, and in theory this could be extended by the Football Association.
The governing body is currently reviewing video evidence but reports on Friday morning suggest it will take no further action.
Hazard apologised for his behaviour and Steven Martens, head of the Belgian FA, says the incident was unacceptable.
"It might have happened in the heat of the fire but professionals are expected to be able to control themselves," Martens said. "They have to be able to control their emotions and when they don't that's unpleasant in general.
"It is 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.
"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 for him. All of us make mistakes in life."
Meanwhile, Redknapp has absolved Hazard of blame for his red card against Swansea, instead branding the actions of the ball boy involved as "disgusting".
Redknapp said: "Hazard toe-poked the ball under the boy's body. Why is the kid lying on the ball in the first place?"
He added: "You can imagine the frustration - you're a player trying to reach a cup final but there's this kid behaving like an idiot who won't give you the ball back.
"Hazard didn't kick the kid, he kicked the ball underneath him, but the whole thing got blown out of all proportion.
"I can think of a lot of players who would have kicked a bit harder than he did. He just toe-poked the ball away. The boy was tweeting before the game that he's a super time waster. The way he behaved was disgusting."
Morgan himself briefly broke his silence on Thursday night, tweeting: "Crazy 24 hours. Spoke to Hazard and I will not be pressing charges. Be in touch."
Despite that, South Wales Police have been obliged to continue investigating the incident after receiving three complaints.
"Three calls have been received from members of the public living in Sussex, Kent and west Wales which are being followed up," a police spokesman said.
Hazard was assumed to have avoided criminal charges when the matter was dropped after he and the teenager met and made mutual apologies.