Ex-England international Carragher was filmed spitting at the family as he drove away after the Reds' 2-1 defeat to Manchester United on Saturday. The 40 year-old was suspended by Sky Sports.
Thompson, who played 48 times at Anfield, reckons personal problems could give an explanation for Carragher's out of character actions.
"Jamie has done wrong he knows that ffs none of you know what's been going on in his personal life and what he's dealing with, let he without sin cast the first stone!" Thompson tweeted.