Jamie Carragher has been suspended by Sky after he was filmed spitting at a football fan's car after being heckled.
Speaking to Sky News, the ex-Liverpool defender called it "a moment of madness".
Carragher, who said he personally called the family on Sunday, said his "biggest regret was that a young girl was caught up in the incident".
When shown the mobile phone footage, which was shot following Liverpool's defeat to Manchester United on Saturday, he said it "felt like an out of body experience looking back on it".
Admitting "what I've done is disgusting", he said "if someone had done what I had done on the pitch I would vilify them".
He said he did not believe the incident "represented the real me", saying "I have brought shame on the name of football. I was a role model, people looked to me."
When he was asked what his children thought of his behaviour, Carragher became visibly upset, welling up with tears.
He went on to say, "hopefully I can get the chance to meet face to face with the family, and apologise to them again".
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A statement from Sky Sports said: "Sky takes this matter extremely seriously and strongly condemns Jamie's actions. We have made this clear to him in person today and suspended him from his duties. It falls well below the standards we expect of our people."