Of the 12 tracks on her new album, 10 of them are labelled as explicit.
Carpenter co-produced it with Taylor Swift collaborator Jack Antonoff, along with John Ryan, who also worked on her previous album, last year's Grammy-winning Short n' Sweet, which topped the charts on both sides of the Atlantic.
In a three-star review, The Times's Victoria Segal said that musically Man's Best Friend was "negligee-thin, surprisingly vanilla".
She added that after the initial cover artwork controversy, it "would have been amazing" if the album "was in fact so subversive that it crushed the male gaze for ever, somehow positioning Carpenter as an avenging angel, a cute pocket-sized gorgon turning men to stone.
"Unfortunately, nothing here justifies that cover image."
The Independent also went for three stars, saying while "there are some sensational songs... too much of the rest struggles for lift-off".
"With Carpenter circling many of the same themes in her lyrics, the hit rate on Man's Best Friend is largely dependent on its song-by-song production," wrote reviewer Adam White.
"House Tour is sensational, a chugging slice of 80s power-pop so instantly catchy that you're able to forgive it holding some of the album's biggest lyrical clunkers," citing some of her more suggestive lyrics.
He added: "Carpenter is above all a brilliant aesthete, her videos and album artwork uniformly inspired."
Meanwhile The I's Emily Bootle called the album "TikTok slop", adding: "She knows sex sells. That doesn't make her a feminist - or make her music any more interesting."
The New Statesman's George Monaghan added: "Her new studio album, Man's Best Friend, may be muted. But she remains the only popstar with comic talent."
The singer-songwriter celebrated the album's release with a Spotify-hosted fan event at Hollywood Forever Cemetery.
She told Rolling Stone magazine the record "wasn't written from a place of 'how do I one-up myself?' or 'how do I re-create something else?'"
She said: "Short n' Sweet was this magical gift; it fed me, and it fed a lot of other people in the world. It felt true to me, and it felt authentic to a lot of other people. It's rare that those line up ever, let alone more than once.
"It unlocked my brain to know myself more and more."