The incident took place in the aftermath of Liverpool's 2-1 loss to Manchester United on Saturday, with the ex-defender being provoked as the scoreline was repeatedly mentioned.
Riise, who spent seven years playing alongside Carragher at Anfield, believes that a line should now be drawn under the spitting controversy.
"Carra has apologized. Phoned the family as well," he posted on his personal Twitter page. "He knows he made a big mistake. He knows! He is only human and we all make mistakes. This is not the Carra i know so I'm certain it won't happen again. Now move on!"
The family of the teenage girl in question has urged Sky Sports not to sack Carragher.