Carly Simon was mostly well received by critics when released. Timothy Crouse, writing in Rolling Stone, stated "Carly's voice perfectly matches her material" and her "...superbly controlled voice is complemented by deft arrangements." Robert Christgau was not as pleased. Grading the album a C-, he wrote "I suppose it makes sense not only for the privileged to inflict their sensibilities on us, but for many of us to dig it." In more recent years, William Ruhlmann, writing for Allmusic, gave the album a three and a half star rating out of a possible five, and stated "That's the Way I've Always Heard It Should Be" and "Dan, My Fling", were the stand-out tracks.
Simon stated in the Ask Carly section on her website that Reunions was her mother's - Andrea Simon - favorite song of hers.