Streisand released "My Father's Song" and its B-side track "By the Way" in Spain retitled "La Canción de Mi Padre" and "Da Paso", respectively.

Simon Price, a writer for The Quietus, liked "My Father's Song" and the other Holmes-written tracks on Lazy Afternoon because he felt they demonstrated Streisand's strengths and abilities on the album.

[1] In the official liner notes of L. azy Afternoon, she stated that the track was "a very personal gift [that] mean[t] a great to deal to me";[2] responding to her comments in a 1988 interview with a Streisand fan, Holmes claimed that the process was simple and that he had only "put in [...] everything that a daughter might want to hear her father say" in the lyrics.

[4] On the standard edition 7" release, "My Father's Song" was accompanied by the B-side track "By the Way", which was written by both Holmes and Streisand specifically for Lazy Afternoon and would later be included on it.

[4] Simon Price of London's The Quietus spoke highly of "My Father's Song" and the two others Rupert-written tracks on Lazy Afternoon ( "Letters That Cross in the Mail", and "Widescreen").