The 20-year-old has started all but one of Kenny Dalglish's ninematches in charge since the Scot was installed as Reds boss until the end of the season last month.
Carragher admits he's been impressed with the level of maturity Kelly has displayed, particularly as Liverpool have contested matches with Manchester United, Chelsea and Everton since he established himself in the first team - and he's confident there is more to come.
"Since Kenny's come in, he's really taken off," the vice-captain told LFC Weekly.
"I remember in his full debut against Lyon (last season) he was outstanding. Then he got injured and when that happens, it's difficult to get another chance.
"Since the United game, England's first-choice right-back (Glen Johnson) has been getting picked at left-back so that shows you how well he's done and how highly he's regarded.
"He's still young and his understanding of the game will develop with experience but he's already a fantastic athlete. I was in the stand against Everton and when he made that run past Leighton Baines, I thought it was Thierry Henry against me all those years ago. It was turbo charged.
"Modern full-backs need to be tall and Martin is very good at defending headers at the back post. His pace means he can get out of trouble when he does make a mistake. That ability to recover with speed was something I never had and he has that in abundance."