The former defender, who retired after 737 appearances for the Reds in May, claims that their local rivals are just as good as his former side this term.
Carragher wrote in his Daily Mail column: "Roberto Martinez has built on the foundations David Moyes put in place and I now genuinely feel Everton are as good as Liverpool — and match the football they play.
"The derbies I played in were physical battles, wars of attrition against Duncan Ferguson. Now it is technical. This season, however, Martinez has coaxed Everton up another level."
Everton host Fulham this afternoon.