"Run" received critical acclaim from music critics. Claire Simpson highlighted the track, Adrienne Day called the song "brilliant", and Jacky McCarthy, from "Billboard", described it as "memorable", due to the band displays "a lush melody, soaring chorus and brooding vocals. Irish musician, Shane O'Neill, said he wept when he first heard it play." Andrew Beaujon added it to "Spin" playlist of "songs you need to know", and wrote it is "the year's most fantastically overblown Britpop power ballad." Mikael Wood from the same magazine compared "Run" to British band Coldplay song "Yellow", as he said it is a "pro-smoking epic [song that challenges the cell-phone-waving majesty of 'Yellow'", a feeling Douglas Wolk of "Rolling Stone" had as well. Josh Modell of The A.V. Club commented it grabs the baton from "Yellow" and "takes it for a weepy, grandiose jog". John Murphy considered its "slow burning delights" replaced the piano chords of Coldplay's "Clocks", which, according to him, started to sound "annoying".