On release, "Billboard" magazine noted "Sue Me, Sue You Blues" as a comment on "the Beatles and their mish-mash", while Stephen Holden of "Rolling Stone" described the track as "a biting slide-guitar showcase for Harrison, its lyric a clever Lennonist diatribe against such monetary quarrels as those that ended the Beatles". In their respective books discussing the former Beatles' first decade as solo artists, Nicholas Schaffner and "NME" critic Bob Woffinden likewise praised Harrison's dobro playing, Schaffner likening it to the "vicious slide guitar work" Harrison had supplied for Lennon on "How Do You Sleep?" Woffinden compared "Sue Me, Sue You Blues" with Harrison's 1966 Beatles track "Taxman", as a composition that showed its author's "impatien with those who come between him and his money", and for that reason, found it "rather out of place" on "Material World". Recalling the album's release in "The Cambridge Companion to the Beatles", Michael Frontani writes: "Harrison's slide-playing is featured throughout, with the swamp-drenched, nocturnal wails of 'Sue Me, Sue You Blues,' in particular, demonstrating his grasp of the form."