Reports suggested that he refused to play in the 3-0 defeat to Manchester City, which would have turned out to be his final game for the Reds.
Mascherano later denied the claims, insisting that he had spoken to manager Roy Hodgson and they both agreed he was not 'right to play'.
Carragher nevertheless believes his former team-mate will have regrets about the way his exit from Liverpool came about.
"Mascherano was great for Liverpool for three or four years and it was a privilege to play with him," said the defender. "But he let himself down badly and that left a bad taste in the mouth.
"If he'd played in that match he would have got a great send-off and it all would have been fine.
"But he ruined that and I think he'll regret it."