Jones, who was renowned for violence during his football career, told our sister station talkSPORT that Carragher should now be sent to the "job centre" as there's no way back for him.
Reports said that some of Carragher's spit hit the face of the girl, who was sitting in the passenger seat.
Mr Hughes, who claims on social media to "hate Scousers", allegedly goaded Carragher over the result, saying "2-1, 2-1, unlucky Jamie lad" while laughing and filming him.
Carragher, 40, apologised to the family and later said his behaviour had been "unacceptable" although he insisted he had not seen the girl in the front of the auto.
They said the former Liverpool defender had personally contacted the family to apologise and had shown genuine remorse for his actions.
Appearing close to tears, he said: "It was a moment of madness".
"You can't condone that behaviour".
"That devastates me more than anything".
He said his "biggest regret was that a young girl was caught up in the middle of the altercation". "I've got a daughter exactly the same age and I can't say how I'd react if someone did that to her".
'I have no excuse and it is devastating for the family involved and my own family, but it is my actions which have brought that on, ' the 40-year-old said.
Appearing on Sky News just moments after he was suspended by Sky, Carragher was made to watch the footage as he appeared for in a excruciating interview live on the channel.
"It falls well below the standards we expect of our people".
Mr Hughes, who says he "hates Scousers" on his Instagram page, spots Carragher driving home after covering the match for Sky Sports and from an open auto window yells at him: '2-1, 2-1, unlucky Jamie lad, 2-1 lad'. We wanted an apology and an explanation.
'He seems contrite. Everyone makes mistakes, we are all human'.
His wife added: "He did seem extremely sorry".
The Countdown presenter branded the reaction to the Jamie Carragher spitting clip as "angry mob bullying" as she spoke to her 545,000 Twitter followers. He's massively passionate about football and he's overstepped the mark and shouldn't have reacted.