[5] I Don't Run features jangling guitar and the interplay of dual vocalists Ana Perrote and Carlotta Cosials, with critics making musical comparisons to The Strokes, The Velvet Underground, The Breeders, Beach House, and The Libertines.

[2][6] Lyrically, the album deals with more mature themes than Leave Me Alone, including the unglamorous realities of awkward romantic situations, infidelity, long-distance romance, and the loneliness of touring.

Several critics noted an increase in sophistication of song structure and precision compared to their first album, with Stuart Berman of Pitchfork praising its "superior songcraft."

"[14] For Flood Magazine, Lydia Pudzianowski wrote that Hinds has "learned a lot since their breakout, resulting in a more confident sound that amplifies what made people love the band in the first place.

[11] In June 2018, Rolling Stone included I Don't Run on its list of "50 Best Albums of 2018 So Far", with Will Hermes praising its "off-handed magnificence" and comparing the drum beats to those of The Velvet Underground's Moe Tucker.