The Smile hitmaker mocks the singers, claiming she will steal the pop crown from them and become "Sheezus".
She particularly ridicules newcomer Lorde by suggesting the teenager will "slay" anyone who gets in her way on the road to stardom, while Allen also calls Lady Gaga a "martyr" of pop music.
In the chorus, Allen sings, "Ri-Ri (Rihanna) isn't scared of Katy Perry's roaring, Queen B's (Beyonce) going back to the drawing, Lorde smells blood, yeah, she's about to slay you, kid ain't one to f**k with when she's only on her debut.
"We're all watching Gaga, L-O-L-O, haha, dying for the art, so really she's a martyr, the second best will never cut it for the divas, Give me that crown, b**ch, I wanna be Sheezus."
Sheezus is the title track from Allen's upcoming album which is due for release on 5 May (14).