Carragher is facing the possibility of losing his job with Sky Sports - where he is believed to collect more than £1m a year - after Saturday's unsavoury incident in which he spat at a man and his daughter was caught on film.
The former Liverpool defender claimed that he had been taunted several times by the man and his 14-year-old child during the road traffic incident, but made a public apology for his actions on Sunday night.
The act took place in the aftermath of Manchester United's 2-1 win over Liverpool at Old Trafford.
Jones, who also represented the likes of Chelsea and Leeds United during his playing career, has slammed the former Liverpool defender for his actions.
"It is cowardly. How has the lad driving it not driven after Jamie, rammed him, dragged him out of the car and beat seven?... you know what I mean," Jones told talkSPORT.
"If someone spat at my daughter sitting in the car, I would have been after them. There is no sitting on the fence here, Jamie is down the road - down the Jobcentre tomorrow. Spitting at 14-year-olds through a window? He is presenting on the TV. For Christ's sake, he is supposed to be one of the top men."
Carragher arrived in London on Monday morning to discuss his future with the broadcaster.