"press" has received generally positive reviews from critics, with many noting the evolution of the rapper's attitude towards the media in the lyrics from previous songs such as "bartier cardi" and her featured verse on husband offset's single "clout"; "nme" called the song "defiant", while "billboard" labelled her as "pressing on" amid "bad press, haters, beefs". "pitchfork" praised cardi being "now fully ready to take aim at any haters" while noting the deviation between "non-stop cut-downs" and "goofier boasts about her money and sexual prowess"; the magazine also stated that the rapper had "sharpened her rapping abilities to deadly effect" in the song.