"Runaway" was well received by most music critics. Robin Murray of Clash called the song "a graceful return" and lauded the singer's mature songwriting. Miranda Feneberger from Paste wrote that the track "channels a soft power". Alexandra Pollard for Gigwise noted in her review of All My Demons Greeting Me As A Friend that "there's an eeriness lurking beneath the beauty of ['Runaway']," adding that "its cavernous clicks and echoes make themselves at home before it bursts into something warmer." She also labeled its lyrics as "unsettling." A writer for Rolling Stone called the song a "viral lullaby." DIYs Sean Murray said that "Runaway" tackled more mature themes, regarding the song to be about "a former love."
