In an interview with English music magazine Mojo, songwriter Matthew Bellamy described "Undisclosed Desires" as one of "some tracks [...] that really take an influence from contemporary R&B, and a little bit from the David Bowie Song "Ashes to Ashes" – heavy beats, syncopation, very melodic, rhythmic vocals," adding that "Dom [Howard, Muse drummer] has done all the drum programming.

"[4] NME commented on the lack of guitar and piano, writing that "the song [is] built around electric drum patterns and some slap bass from Chris Wolstenholme.

"[8] Reviewing for NME, Ben Patashnik noted "Undisclosed" as evidence of the band "try[ing] to reignite the low-down R&B of ‘Supermassive Black Hole’," which he also suggests "backfires.

"[9] Mojo, on the other hand, identified "Undisclosed" as one of the highlights of The Resistance, along with "United States of Eurasia" and "Uprising".

The video, directed by French duo Jonas & François, depicts all 3 members of Muse in a rather unusual room where there are wires lying and hanging everywhere.