Alix Buscovic of BBC Music described the song as a "power-dressed Europop floor-filler that channels early Depeche Mode and the PSB", which was made with "theatricality" and "a brooding demeanour", but criticized the lyrics.

[1] PopMatters reviewer Joe Copplestone compared the track to New Order, deeming it "gleefully era-authentic" and commending its commercial appeal.

[2] While commenting on the "lack of depth" of the lyrics in Happiness, Sam Shepherd from musicOMH praised Anderson's work, with the song's mix of "Eastern Bloc industrial pomp with Eurovision disco-pop" having a "surprisingly engaging effect.

"[3] In the Drowned in Sound review, Andrzej Lukowski considers "Sunday" to cross into "boyband territory", having "a decent hi-NRG synth line", nevertheless a "desperately gauche" feature.

Theo Hutchcraft stated that the video follows a similar theme to the group's others, adding "it's nice to go away to film the videos because you live in a different world for a few days[...] We go to an exotic, beautiful place, think of a theme that no-one else will understand except us, and surround us with women so people won't ask us what it's about!