Saliba, 19, is still waiting for his Gunners debut despite arriving in north London last summer following a £27million transfer from Saint-Etienne in 2019.
"Arteta can get on the right path by working with the top class youngsters emerging from his academy, assisted by the correct assortment of more experienced players," Carragher told The Daily Telegraph.
"Bukayo Saka is one of the most exciting young players in England.
"I am surprised we have not seen more of highly-rated teenage defender William Saliba since his signing from Saint-Etienne, even though the youngster was sent off playing for the club's Under 21s earlier this week.
"Arteta must stake his reputation on them as he eases out those unsuited to the philosophy, building a younger, more active team over the course of two or three windows to correct the errors of the last five or six."