Carragher was filmed spitting in the direction of a car in which the driver was filming as he goaded the former Anfield star about Manchester United's 2-1 win over Liverpool at Old Trafford on Saturday night (AEDT).
The 14-year-old sat in the passenger seat claimed some of the spit had hit her and, in a statement, Sky said they had suspended Carragher for actions "well below the standards we expect of our people".
Speaking on Sky News after his suspension was announced, Carragher, who has called to apologise to the family, said: "You can't condone that behaviour in any way shape or form.
"[It was] a moment of madness, it is difficult to explain. Watching those clips back it feels like almost an out of body thing. A moment of madness for four or five seconds.
"You're actually thinking to yourself, 'Why did you react like that?' That's part of being a public figure. I just have no excuse. I'm devastated for the family involved and my own family.
"My biggest regret is for the 14-year-old to be caught in the middle of this altercation with the father. That devastates me a little bit more than anything else.
"I can't go back, hopefully they accept [my apology]."
Asked to explain why he should remain with the broadcaster, Carragher, who said he has not offered his resignation, replied: "There's no doubt what I have done is disgusting, I'm getting vilified and rightly so.
"What I would hope for the public who have known me for almost 25 years in the public eye is that five seconds of madness will not take over everything I've done now.
"Hopefully going forward I can show the real me. I don't think that is a real representation of me."
In addition to being suspended by Sky, Carragher has been dropped by Danish broadcaster TV3 for their coverage of United's UEFA Champions League last-16 second-leg clash with Sevilla at Old Trafford.
"Jamie should have been at Old Trafford for us and we have taken him off that," TV3's head of sport Peter Norrelund told Danish publication BT. "It would have been like sending him into a lion's den. I have seen the video and it certainly doesn't look good.
"It is a big story in England and I wouldn't have thought that sending him to Old Trafford would have been a good idea, and then we want his reaction and explanation for what has happened too.
"I don't know what will happen [long-term]. It is not good behaviour but we are all just human beings. We want to hear from him what happened.
"That is the same for all employees – whether it is the receptionist or Jamie Carragher – we are not going to sanction someone until we've heard from them what happened."