In the video, the father repeatedly mentions the score and Carragher is heard to say, "Alright", before appearing to spit at the auto alongside his vehicle. The girl then wound down her window before her father shouted "Unlucky Jamie lad".
Carragher, 40, apologised to the family and later said his behaviour had been "unacceptable".
Sky realise he's good box office, he's great business, and I'd be very surprised [if he was dimissed]. I wish she wasn't involved.
"I've done a lot of stupid stuff, and we all get stick, but to do that", he continued. "That devastates me more than anything".
"Hopefully the family can accept that apology from me".
The incident followed Saturday's lunchtime match at Old Trafford and was caught on mobile phone and obtained by the Daily Mirror, which splashed with the story on its front page this morning. Say that was me, I think my position would be under fire and I think [his] will be.
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It is ironic that Carragher resorted to such vile behavior when he himself used to look down upon footballers who spat at one another.
JC: It was a moment of madness. This won't be nice for them, especially the 14-year-old girl.
A Danish television channel has also chose to pull the ex-defender from its coverage of Man United's meeting with Sevilla at Old Trafford on Tuesday night.
Greater Manchester Police said they had not received any complaints regarding the incident.
Carragher wrote: "As usual, there have been a number of people who have said, 'It is the worst thing that can happen on a pitch". Once you've made such a mistake it's about how you act now.