The accompanying music video, directed by Colin Tilley, depicts Katy surrounded by winds, while in a room alongside a tied-up man.

[1] Jenn Pelly from Pitchfork Media commented: "It's an aggressive take that rips slow, propulsive beats through the otherwise melodic dance track, evolving it into something noticeably more physical.

[3] Having a length of three minutes and twenty seconds (3:20),[4] "Witches' Brew" is styled in the musical genre of electro, incorporating diverse elements of breakbeat in its composition.

[7] Alex Denney of music publication NME deemed its beat "strident" and compared its synthesizer arrangement to sounds from a pinball machine, though he had a slightly more polarized reaction to the song's "hackeneyed arena-rave"-based chorus.

[11] Gavin Martin of the Daily Mirror believed in the song's potential to be received as positively as the first two singles from its parent album, due to its "creamy melody and soulful come on".