When Mitchell was working on new material in Britain, Robert Plant visited the house she was staying at with the intention of finding potential songs to record.

Considine of Rolling Stone thought that the song showcased "the similarities between her [Mitchell's] voice and Peter Gabriel's", saying that they "illustrate[d] the shifting confidences of shared intimacy".

He highlighted moments in the song where the two swapped lines within a stanza, which he thought was an effective means of demonstrating the fluctuations in balance within a relationship.

[2] Uncut commended the drumming of Manu Katché and also praised the song's vocals, saying that "Gabriel and Mitchell's voices tie together to the point of being inseparable.

[6] Greg Quill of the Toronto Star was more critical, saying that "My Secret Place" was "arguably the least appealing song on the album", although he praised Gabriel's "strong counterpoint" vocals.