[12] Christopher Monk of musicOMH pointed out the "scuttling percussion, Nile Rodgers-esque guitar, [and] atonal piano stabs" of "Exploitation", while Jim Carroll called the lead single "a track where the groove is simple and sparse, works with considerable panache.

[14] St. Asaph deemed "Unputdownable" to be "a traditional Murphy extended metaphor—lover as page-turning book", continuing on to say that "'House of Glass' delivers grand statements, often set stark against the music".

[14] Monk described "Hairless Toys (Gotta Hurt)" as a "lovely ballad" and thought "Unputdownable" to "end the album on a downer, before it transforms into something quite uplifting".

"[21] Pitchfork called Hairless Toys "the most cerebral work of Murphy's decades-long career" and described it as "all gleaming and immaculate from a distance, sharp and shattered if you get too close.

[12] Electronic Beats called the album "a decisive step forward and a definitively experimental pop record, delivered with a confidence that defies the brevity expected of chart fodder.

[20] Mixmag also noted the album's integration of "elegant deep house [...] country-flecked soul, and idiosyncratic downtempo", and called it "a career high".

[19] Writing for The Irish Times, Jim Carroll said the eight-year gap between albums for Murphy "has not lessened her knack for beautifully finessed tunes pulled together with sublime electropop belts and braces.