According to the sheet music published by Musicnotes.com, "Don't Tell Me" is set in the time signature of common time, with a moderate tempo of 100 beats per minute. It is composed in the key of D major with the singer's vocals ranging from the lower octave of G3 to the higher note of A4. The song follows a basic sequence of D–Am–C–G as its chord progression. Ben Greenbank from "Sputnikmusic" described the track as a "country meets dance" song with trip hop beats, accompanied by acoustic guitar riffs. Chuck Arnold of "Billboard" described "Don't Tell Me" as a "twangy trip-hop" track. The song begins with a "plucked" guitar riff in a jagged stop/start beat, with the arpeggios reminiscent of country music. Every fourth beat is followed by a small silence that eventually builds into the chorus.