[17] Editors at AllMusic rated this album 4 out of 5 stars, with critic Mark Deming writing "Cousin represents a genuine shift for the band as they've ceded some control over their recording process for a change", resulting in "a powerful, affecting work that once again shows how many great things Wilco can do".

[21] Ryan Dillon of Glide Magazine praised this music for "Wilco's most complex and evocative album in years" and blending artsy or avant-garde tendencies with accessible songwriting[22] and he chose "Sunlight Ends" as one of the best songs of the week, calling it "a moody example of the band's experimentation, an electronic drum pattern sets the tone for dancing guitar strings and sinfully sweet vocals".

[25] Ed Power of Irish Examiner gave Cousin 4 out of 5 stars, characterizing the music: "it's catchy and often very warm but full of the avant-garde wrinkles that have led critics to herald the Chicago outfit America's answer to Radiohead".

[26] Lauren Murphy of The Irish Times gave the same score, calling it "Wilco's most progressive album in years, dappled with a sumptuous melancholic hue that drapes itself over songs such as Ten Dead and the sombre, minor chord swoon of Levee".

[27] A feature from Louder Sound saw Sam Walton calling this the best Wilco album since 2004's A Ghost Is Born and the choice to enlist Le Bon "the most elegant producer-led transformation of the past 25 years".

[30] Writing for No Depression, Kyle Peterson calling this release not "a return to the grand statements of the late 1990s and early 2000s so much as a distinctive entry that still fits comfortably in the band's latter-day output".

[35] Rolling Stone featured a favorable review from Will Hermes, where the critic praised the production and how "part of Wilco's magic is its mutability... and how artfully it always cleaves to Tweedy's narrative voice, one of the most companionable in modern song, even when he's channeling flawed characters, which he frequently is".

[36] Michael Gallucci of Ultimate Classic Rock called this work an "aural tour de force", continuing that "the music, drifting among the avant-pop playground Wilco has spent the past two decades traversing, suits the occasionally despairing, often hopeful mood".

[37] In Uncut, Tom Pinnock scored Cousin 4.5 out of 5 stars, praising the production and writing that this music is "deliciously weird and intoxicatingly angular, but it still sounds like a Wilco album, not a Le Bon collaboration".