In an interview with MusicRadar, Corgan stated, "I have all of these vintage keyboards that we just crank out when I need something, so I don't really know what's on here. It's some super, highly obscure '70s keyboard." He added, "The arrangement is kind of like classic MTV, circa 1994. You start with the acoustic and then the band kicks in grunge."
The track has received positive reviews. Loudwire praised the track's sound, stating "Acoustic guitar and orchestral swells dominate the beginning, along with Corgan’s tortured vocals (which actually have a better, more polished sound than on other recent works). Once the full band kicks in, you realize that this is the standout track on the album. 'The Celestials' employs all the elements that make a classic Pumpkins song, and is likely the best released under the name in over a decade. Corgan caps off the tune by matching the line "Everything I want is free" with a beautifully reserved lead guitar riff."RedEye favorably compared it to one of the band's biggest songs, "Disarm", from their album Siamese Dream, calling it a "...nod to the Pumpkins' past. Its acoustic guitar and orchestration make it, if not a sibling, then a distant cousin to the classic "Disarm". Similarly, CraveOnline compared it to the most acoustic aspects of their Mellon Collie and the Infinite Sadness album and said that "...The song is catchy but with a injection of prog-rock that keeps it from collapsing on itself."