The Constant received mixed to positive 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 63, based on 11 reviews, which indicates "generally favorable reviews". Heather Phares wrote for AllMusic that "much of The Constant finds I Blame Coco trying on different sounds, wanting to make artsy music as much as they want to deliver bona fide hits", but later concluded that the album "has enough strong moments to make it a promising debut from a group with plenty of confidence, personality and potential." Joe Vogel of PopMatters praised the album as "a worthy and promising debut", dubbing it "a young album that avoids certain risks , but there is a vitality and ambition to it that is rare and refreshing for pop music." The Daily Telegraphs Lucy Jones referred to the album as "a well-crafted and impressive debut", adding that "lthough the album doesn't quite ignite, Sumner's innate talent shines through." Drowned in Sound's Neil Ashman opined that "Coco's voice is of a strangely husky tone, generally keeping to the lower register, never sustaining notes for show and pretty reminiscent of her father in its rhythm and intonation." However, Ashman commented that "until Coco can hit upon this kind of refinement of her influences in a more general sense, she seems destined to be known firstly for who her father is and only secondly for her own artistic achievements." Ben Weisz of musicOMH noted that "The Constant isn't exceptional, but it does demonstrate a sophistication which sets her apart from the twee pop of some of her rivals." The Guardians Caroline Sullivan viewed the album as "essentially a mildly promising debut by an artist who can write a tune but not yet with any great distinction", while calling the lyrics "wordy and pained". BBC Music reviewer Sarah Bee felt that "Sumner's voice seems more suited to the loping of reggae than the skittering of electro-pop and its cousins and maybe she'll relax into similar territory next time around. There's nothing radical here, but revolution isn't all it's cracked up to be." In a review for the NME, Alex Denney described "Caesar" as a "good-ass pop tune", but stated that "for the most part The Constant boils down to a thin chart gruel, too lumpenly pitched between the Carling Academies and the cattle-grid nightclubs to leave a mark." Ian Gittins of Virgin Media found that Sumner "has spectacularly inherited her father's idiosyncratic musicality, with her husky, masculine tones and mannered whoops and yowls illustrating that she has paid close attention to her dad's vocal repertoire." Louisa Emery of The Wharf expressed that "Coco has created an album that shows she is more than a over privileged kid playing popstar, even if it will do little to shake off her Sumner stigma." Neil Condron of Clash magazine characterised the album as "redictably pristine, ultimately inessential". The Observers Killian Fox argued that "the album ends up feeling oddly flat. We are left with a sense of excitement unfulfilled."
