Anywhere I Lay My Head received mixed reviews from music critics. At
Metacritic, which assigns a
weighted mean rating out of 100 to reviews from mainstream critics, the album received an average score of 58, based on 35 reviews, indicating "mixed or average reviews". Priya Elan of the
NME called the album "brilliant" and wrote that "just like
Lou Reed with
Nico and
Serge Gainsbourg with
Brigitte Bardot, Sitek has effortlessly translated Johansson's magnetism on to record", while comparing her "deep" voice to "latter-day
Ronnie Spector's street-savvy tone".
The Observers
Barney Hoskyns commented that Johansson's "blankly androgynous alto timbre is nothing special, but that barely matters", praising the album as "a bravely eccentric selection and a captivating homage to a singular writer".
The Guardians Dorian Lynskey described Johansson's voice as "a supple, languid instrument offering hints of Nico,
Kim Deal and
Martina Topley-Bird" and stated, "You might wish there was more from Waits' 70s barfly period [...] but it's a measure of this album's surprising allure that you're left wanting more."
AllMusic reviewer
Stephen Thomas Erlewine found Johansson to be "surprisingly deep and brittle as a singer", concluding that the album "doesn't quite work, but it can't quite be dismissed, either: unlike so many actor-turned-singer records, there's not a hint of vanity to this project and it's hard not to marvel at its ambition even as it fails." Mikael Wood of
Spin wrote, "Beyond the fact that her voice is deep enough for her to front
Crash Test Dummies, there's nothing particularly compelling about Scarlett Johansson's singing", adding that "her vocals are buried deep beneath [...] Dave Sitek's mountain of reverbed space-gospel noise." Nevertheless, Wood opined the album is "[n]ot your typical Hollywood vanity project". Chris Willman of
Entertainment Weekly remarked, "In burying Johansson's vocals so deeply in the druggy ambiance, producer David Andrew Sitek [...] means well but ends up obscuring Waits' great tunes." Stephen M. Deusner of
Pitchfork viewed the album as "a
Brooklyn update on vintage
4AD bands like
This Mortal Coil or
Cocteau Twins", but noted that "[t]he only thing we've learned about her is that she really, really likes Tom Waits. That's more than enough to avoid catastrophe, but not quite enough to make
Anywhere I Lay My Head much more than a curio."
Rolling Stones
Will Hermes critiqued that "Johansson's voice is unremarkable and her pitch sometimes unsteady", dubbing her "a faintly goth
Marilyn Monroe lost in a sonic fog". Dave Hughes of
Slant Magazine expressed that Johansson is "neither a particularly interesting nor a particularly skillful singer, and she spends much of the record locked into a sub-Nico hum that's quite a bit less charismatic than her husky line readings might suggest." Alex Denney of
Drowned in Sound concluded, "Perversely given the record's comprehensive musical overhaul it's perhaps a surfeit of respect for the source material that proves
Anywhere...s undoing; for all its undoubted accomplishments there's a lingering suspicion that this is too safe, too respectable a record to do justice to an artist who remains forever mid-topple from the bar stool in the popular consciousness." ==Commercial performance==