Lyrically, the song is about a day in Madonna's life with some portions of it directed at her ex-husband, film director Guy Ritchie, when she sings about a failed marriage.
The song received generally favorable reviews from music critics who praised Minaj's appearance and its personal lyrics.
Madonna's manager Guy Oseary had contacted Martin Solveig wanting to know if he would be available to work with the singer, to which he responded affirmative.
Madonna expressed her thoughts about the composition, including the instrumentation to be used as Solveig added, "at some point she wanted to choose the sound of a snare drum or a synth and that kind of stuff.
[4] Regarding having Minaj feature as a guest vocalist, Madonna explained that she wanted to collaborate with female singers she believed had a "strong sense of themselves".
[6] Ron Taylor did the vocal editing for the track while Michael Turco added the outro music for The Demolition Crew.
[6] "I Don't Give A" is a midtempo "pop-flavoured"[7] electro-funk[8][9] song with "ballsy" electronic hip hop and industrial beats.
[10][11] Tracklisted after the initial dance tunes in MDNA, the mood for the song is dark and somber, with a Sturm und Drang chorus and backed by an orchestra that The New York Times reviewer Jon Pareles compared to composer Carl Orff's cantata, Carmina Burana.
This is enunciated with the lyrics addressing Ritchie and tabloids, along with some of Minaj's verses being directed against pop singer Lady Gaga, with whom Madonna had been compared to previously.
Neal McCormick of The Daily Telegraph called it "an album highlight", writing that "there is real energy to this Martin Solveig production, though Nicki Minaj's explosive rap rather shows up Madonna's more static delivery".
[20] The Village Voice's Maura Johnston was also complimentary about Minaj, writing that, "[She] lays down a couple of rhymes that are by no means the best in her vast catalog, but her sudden presence shows that the music isn't the song's biggest weakness.
[5] For Matthew Perpetua of Pitchfork the song showed how Madonna's strong rapping was upstaged by Minaj, "who turns in an entertaining performance that is nevertheless below the standards of her usual features".
[23] Nick Bond of Sydney Star Observer wrote that the song is "not her most GFC-friendly track", but explained that "Musically, it's the damp squib that was Hard Candy done right.
[24] The performance of the song closed the show's first segment known as Transgression, and found Madonna playing the guitar while Minaj appeared on the backdrops sitting on a throne singing her verse.