Lisa Oliver of Stylus Magazine commented "Run" has "raw tenderness", and listeners should not "listen to it in public—unless openly weeping in front of colleagues or commuters is not a concern." Christian Carey of Junkmedia.org called it, along with another song of "Final Straw" ("Grazed Knees"), a "symphonic pop gem", and the "most memorable" track of the album. Steven Gozdecki of Neumu.net called it "centerpiece" of the album and a "brilliantly entrancing" tune, and also noted it is "the song that Coldplay dream of making". Gozdecki complemented with "is a moving ballad that benefits from the absence of that other band's dreadful, Dave Matthews-esque voice and omnipresent electric piano." Natasha Perry considered it to be a song "that sends shivers down the spine with a haunting verse and uplifting chorus." A reviewer for Sputnikmusic compared it to Snow Patrol song "Chasing Cars" (2006), which was described as "beautiful".