In footage which was widely shown on British media, Carragher is shown winding down the window of his car and spitting at another vehicle following Liverpool's 2-1 loss to Manchester United on Saturday.
Carragher, 40, said he had apologised to the family, admitting he "lost (his) rag". He had been covering the game as an expert for British broadcaster Sky Sports.
"Totally out of order & Ive apologised personally to all the family this evening. I was goaded 3/4 times along the motorway while being filmed & lost my rag. No excuse apologies," Carragher posted on Twitter.
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