[7] It grew (like "Sun King") from the F♯m7–E changes from Fleetwood Mac's "Albatross" with McCartney arranging instrumental and vocal parts and George Harrison adding a descending two-part lead guitar accompaniment to the verse and a countermelody in the bridge.

[8] Alan W. Pollack states that "the counterpoint melody played in octaves during the Alternate Verse by the bass and lead guitars is one of the more novel, unusual instrumental touches you'll find anywhere in the Beatles catalogue.

Richie Unterberger of AllMusic called it "one of the Beatles' most powerful love songs",[16] Stephen Thomas Erlewine of AllMusic described the song as "heart-wrenching soul"[3] and Roy Carr and Tony Tyler called it "a superb sobber from misery-expert J. W. O. Lennon, MBE.

"[17] Author Ian MacDonald praised "Don't Let Me Down" and declared that "this track vies with 'Come Together' for consideration as the best of Lennon's late-style Beatles records".

[19] No official producer's credit was included for the single release owing to "the confused roles of George Martin and Glyn Johns".