Tottenham 0 // Real Madrid 1 (Real Madrid win 5-0 on aggregate)
Trailing 4-0 from last week's quarter-final first-leg, Spurs tried to prove the return match was anything but a dead rubber and saw three first-half penalty appeals turned down by the referee Nicola Rizzoli.
Gareth Bale, Luka Modric and Roman Pavlyuchenko all went over in the box but their screams and those of a packed White Hart Lane fell on deaf ears.
Pavlyuchenko also wasted a glorious chance on 37 minutes to put Spurs ahead, while Real also threatened in a pulsating first half which belied their 4-0 first-leg advantage, with Mesut Ozil and Sergio Ramos going close.
Cristiano Ronaldo then rubbed salt into the wounds on 50 minutes when Gomes spilt the forward's 30-yard strike into his own net to settle the tie and enable Real set up a mouthwatering semi-final against Barcelona.
Tottenham had chances to salvage some pride late in the game, with the substitue Jermain Defoe seeing a stoppage-time strike blocked by Iker Casilas after more good work from Bale.
But the debutants, who have lit up the competition with wins against AC and Inter Milan, went out with an aggregate scoreline that does not flatter their Spanish opponents.
The London club may struggle to qualify for next year's competition.