The report, which makes the front page of Monday’s newspaper, says Carragher’s Range Rover had pulled up beside her United-supporting dad’s car in heavy traffic after Liverpool’s 2-1 defeat by Manchester United on Saturday.
“I would like to apologise for my actions which were totally out of character,” said Jamie.
“What I did was wrong and I have since personally apologised to the family involved.”
Video footage shows how the pair exchanged, before the dad shouted: “Unlucky Jamie lad!” and “2-1!”
Jamie added: “I was continually goaded and verbally abused numerous times whilst being filmed in slow moving traffic and reacted in a way that is of course regretful.”
Sky Sports said: “It’s unacceptable behaviour and we will be addressing it with Jamie.”
Update: Jamie speaks live on Sky News