The Mirror reports Carragher was caught on camera aiming mouthful saliva at the passenger window of a car containing the 14-year-old Manchester United fan and her dad after Saturday's Red Devils victory over the Anfield outfit.
She claimed the spittle hit her on the forehead, making her cry.
The dad told how he had been having “a bit of banter" with the former defender which turned ugly after he mention the 2-1 scoreline. And he insisted the TV star must have seen his daughter was in the passenger seat.
Carragher, who had been covering the match as a SKY Sports pundit, last night phoned the girl and her father and said: “I just want to apologise and I hope you are OK." The youngster told him: “OK, thanks for apologising."
He had earlier admitted he was in the wrong but claimed he lost the plot after the ribbing went on too long.
The 40-year-old said: “It was a bit more than, 'Hiya Jamie, it was 2-1'. It went on for two or three times. I drove away at first and it just continued. I lost my head. I shouldn't have done it but I was thinking what is a grown man doing, carrying on like that two or three times with his daughter in the car?"