"Hopefully I'm judged not right now but over a longer period of time", the 40-year-old told BBC Sport.
"I'll speak to the family again".
He later is reported as having telephoned the girl and her father, saying: "I just want to apologise and I hope you are OK".
"I just have no excuse, it's devastating for the family involved".
Carragher was today suspended from his duties as a Sky Sports pundit after spitting at the girl, the broadcaster announced.More news: Apple Acquires Digital Magazine Subscription Service Texture
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Carragher's Sky colleague and former Manchester United defender Gary Neville tweeted his support.
"He said he wanted to take the chance to tell Carragher how badly he had behaved and to look at himself before trying to judge anyone else". No matter what the circumstances you can't ever behave like that.
"The biggest regret was that a young girl who wasn't involved was caught up in the incident". The spitting incident incited rage from football fans across the world, with the pundits to labelling it as shameful on Carragher's part.
Sky said Carragher's actions were "well below the standards we expect of our people".
SH: But from your point of view, do you feel, after those actions, you deserve to their on Monday Night Football, as a face of the broadcaster, a face of football, a role model, do you deserve that position?
"I am speaking to people at Sky and working at the best way forward. He's massively passionate about football and he's overstepped the mark and shouldn't have reacted", he wrote.
"He said it was disgusting behaviour and Carragher should receive a full punishment for what he's done". I know it has put my family and friends in a hard position.