Sports blogger Adam Joseph shared footage of the incident:
Byrne and Davidson's report supplied criticism from the teenager's mother, who said she was "extremely angry and disappointed" with the 40-year-old.
The report also provided further quotes from Carragher about the incident: "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?"
According to the Daily Mail's Dominic King and Charles Sale, the saliva hit the girl in the face, prompting her to cry. "I have never been spat at by anyone before," she said. "I thought, 'Why has he done that?' I thought I had done something wrong."
"It is unacceptable behaviour, and we will be addressing it with Jamie," a spokesperson for Sky said.
Carragher had been at Old Trafford in his role as a Sky Sports pundit and saw his former side go 2-0 down in the first half after two Marcus Rashford goals.
An own goal by Eric Bailly gave Liverpool a chance of snatching a point from the clash and made for a tense finale.
But United eventually claimed all three points to strengthen their grip on second place in the Premier League.