Upon release, "Roar" received generally positive reviews from critics. Gerrick D. Kennedy of the Los Angeles Times called the track a "sweet, poppy confection with a bit of bite"; he also praised Perry's vocals.[23] Rolling Stone also gave the song a positive review, saying, "With its easy poppy beat and repeated refrains of 'You held me down but I got up,' and 'You're gonna hear me roar,' the lead single strikes a determined note for the new album."[2] James Montgomery of MTV described it as "undeniably genuine", writing: "It is personal, it is powerful, and, with its combination of sonorous hooks and searing sentiment, it is certainly one of the more perfect pop songs to come down the pipeline in quite a while.[19]
Michael Cragg of The Guardian called it "a massive single from a massive pop star who knows exactly what she's doing".[24] Andrew Hampp from Billboard had a positive response to "Roar", claiming it was a "stylistic return to the arena-sized singer-songwriter formula that made her debut on One of the Boys", but criticized the lyrics, saying they "rarely rise above easy clichés and rhymes and that the stomping mid-tempo beat leaves a little to be desired in the BPM department".[1] Melinda Newman of HitFix called the song a "fierce, fun anthem" and complimented the song as a "great change of pace" for Perry.[25]
Charley Rogulewski of Vibe called the track a "sure-to-be radio hit with an empowering theme similar to her track "Firework".[3] Katie Aktinson from Entertainment Weekly also compared it to "Firework", claiming that its lyrics "will likely make the song a fall-football anthem", and jokingly said that "the Bengals should send her a check now".[26] Chiderah Monde from New York Daily News referred to the chorus as "catchy" and said the song was "another certified anthem" for Perry.[27] James Shotwell from Under the Gun Review said the song takes a "more powerful approach" than Perry's previous material.[28]