Albion crashed out of the Carling Cup after a 2-1 defeat to Everton - despite having one foot in the fourth round.
Chris Brunt gave a much improved Albion side the lead in the 57th minute after Peter Odemwingie had been felled in the area.
But with only seconds remaining Marouane Fellaini's 18-yard volley levelled the scores and sent the tie into extra time.
Everton captain Phil Neville then secured a passage into the next round for the hosts when he curled in a fine effort two minutes before the break in the additional 30 minutes.
The Baggies pushed forward again after the break, but were unable to find a leveller to send the game to penalties.
Roy Hodgson made nine changes to the side which was comprehensively beaten by Swansea at the weekend and singled out praise for youngsters George Thorne, Joe Mattock and Billy Jones.