Everton's long wait to win a trophy will not end with the League Cup after Frank Lampard's men were well beaten 4-1 by Bournemouth on Tuesday, as Brentford bowed out on penalties to League Two Gillingham.
In the first of two meetings between the clubs in five days, Bournemouth got the better of two much-changed sides as Jamal Lowe, Junior Stanislas, Emiliano Marcondes and Jaidon Anthony struck on the south coast.
Demarai Gray briefly gave the Toffees hope when he reduced the arrears to 2-1 early in the second half.
But Everton have now won just once in their last seven games with the FA Cup their only hope of ending a 28-year drought without silverware.
Brentford suffered the biggest shock of the night despite taking a third-minute lead through England World Cup hopeful Ivan Toney.
The Gills had just one shot on target but made it count when Mikael Mandron headed in an equaliser 15 minutes from time.
Mikkel Damsgaard is going to Qatar with Denmark, but he was the only man to miss in a high-quality shootout as the visitors won 6-5 on penalties.
Leicester continued their upturn in form with a comfortable 3-0 win over fourth-tier Newport County.
