The track contains a brass sample from "Hippy Skippy Moon Strut" by Dave Cortez & The Moon People, and a vocal sample "The Cissy's Thang" by The Soul Seven. Its instrumentation incorporates keyboards, guitar, drums, percussion, and horns. The arrangement of the instruments on "Ain't No Other Man" was described as "raw" and "ass-shaking". Several critics complimented the mixture between old and modern materials; Jody Rosen from "Entertainment Weekly" claimed that the jazzy melody from the track suited Aguilera perfectly, while Dorian Lyskey of "The Guardian" deemed the melody of "Ain't No Other Man" "fun" and "crispy".