Firmino joined Liverpool from Hoffenheim in the summer of 2015, and the 26-year-old has scored 42 goals in 124 appearances for his English club in all competitions.
This term, the Brazil international has managed 19 goals in 35 appearances in all competitions.
Carragher has even compared Firmino to the club's former striker Luis Suarez, insisting that he offers things that "nobody else can".
"Firmino has been a revelation this season. I actually think he is one of the most underrated players in the Premier League. He has always been Liverpool's number one striker but what he has been adding is the goals," Carragher told Sky Sports News.
"He can actually match up to the other strikers now goals-wise and still bring all the other stuff that he brings. Even without the goals, I don't think Klopp would ever look to replace Firmino.
"If Harry Kane gets 40 goals and Firmino gets 20, he would still be one of - if not the first - name on the team sheet because of what he does off the ball. Klopp appreciates all of the extra things that Firmino brings to this Liverpool team that nobody else can.
"There is something about South American players. They just seem to be able to keep going. Klopp said recently that Firmino has one rest day after a game and then he's back on it in training and that's exactly how Luis Suarez was. He never wanted a rest even in training. That is just how some people's bodies are - they seem to be able to deal with anything."
Liverpool will attempt to return to winning ways in the Premier League when they visit Southampton on Sunday afternoon.