Carragher has been suspended by Sky after he was filmed spitting at a football fan and his 14-year-old daughter while driving away following the Reds' 2-1 defeat to Manchester United.
He said: "You can't obviously condone that behaviour no matter what.
"In any way shape or form, where you are, who you represent.
"I've let Sky Sports down, my family and the family involved.
“It was a moment of madness, it's difficult for me to explain.
"It's just that moment of madness for four or five seconds. No matter the circumstances, you can't ever behave like that."
He continued: "I called the family and they were upset.
"The biggest regret, certainly, is for the 14 year old girl to be caught in the middle of this, and my altercation with the father.
"It's my biggest devastation that a young 14 year old has become embroiled in this.
"I've got a daughter the same age...it's difficult to find the words for the way I'd react. It is me biggest regret of course, but all I can do right now is apologise. I can't go back. Hopefully they accept that. I'd like to apologise once more to them all."
Asked if he should be sacked, Carragher responded: "Well again, it doesn't matter if I say yes or no. That's down to the powers above.
"Hopefully I can show people over the next days and weeks the real me. Hopefully a moment of madness won't cloud people's judgment of me, my character, my career
"The big thing I'm disappointed in, obviously, is the daughter.
"I don't want to give a reason or an excuse. It happened two or three times, but I've had that. That's part of being a public figure and I've never reacted like that.
"I can't explain why I reacted like that...it's not happened before, it won't happen again.
"It's devastating for them (the family), it's devastating for me and my family.
“I must try to improve my actions moving forward."