Substitute Hanna Bennison’s late strike with virtually the last kick of the game was mere consolation as a much-changed Blues exited the competition this season.
Brian Sorensen made six changes form the side that was narrowly defeated by Arsenal on Sunday, including starts for both Martina Piemonte and Toni Duggan.
But it was clear to see who was chasing something out of this game, as goals from Sam Tierney, Deanne Rose, Missy Goodwin, Jutta Rantala and a Shannon O’Brien penalty were only replied when Bennison converted Megan Finnigan’s low cross in the sixth minute of second-half injury time.
The hosts dominated throughout but found Courtney Brosnan in stubbornly defiant form.
But even some exceptional saves from the Republic of Ireland’s No.1 couldn’t stop the eventual onslaught that found the Toffees 3-0 down before the half-hour mark.
Goodwin made it four three minutes after the restart as Sorensen introduced Clare Wheeler, Finnigan and Bennison on 56 minutes.
The latter two combined well to pull one back at the death but not before Brosnan performed more heroics, this time saving a second Leicester penalty.
The stopper could do little to prevent Rantala’s deflected strike to make it 5-0 to the Foxes, with Everton’s attention now firmly on the WSL fixture against former Blues manager Willie Kirk’s side at Walton Hall Park this Sunday.
Kick off for this encounter at the home of the Blues is 12.30 (BST).