Tottenham keeper Gomes fails to retrieve his mistake from Ronaldo's shot
Spurs boss Harry Redknapp made predictably defiant noises about the possibility of overturning Real's 4-0 lead from the first meeting at the Bernabeu - but in reality
this was never a serious option against Jose Mourinho's side.
And so it proved as Real were helped on their way towards an 'El Clasico' confrontation with La Liga rivals Barcelona in the last four by a nightmare moment from Spurs keeper Heurelho Gomes.
Spurs had failed to make any inroads into Real's lead when Gomes fumbled a routine effort from Cristiano Ronaldo into the net five minutes after the break to complete the formalities and take Mourinho a step closer to a Champions League final with a third club.
Redknapp's players did everything in their power to clear the huge obstacle in front of them and were unfortunate not to be awarded an early penalty when Luka Modric looked to be brought down by Xabi Alonso.
It was a rare moment of discomfort for Real as Spurs' Champions League campaign fizzled out in low-key fashion in front of their own supporters, who showed their appreciation for the efforts of their players in Europe with warm applause, even in disappointment, at the final whistle.
Spurs must now turn their attentions towards overhauling Manchester City in the race for a top-four place to ensure they return to this stage next season - but they can take great credit from the manner in which they have acquitted themselves in Europe's elite competition.
The night Inter Milan were soundly beaten at White Hart Lane and the victory against AC Milan in the San Siro will live long in the memory. They were undone, however, by Real's superior quality as well as the self-destruct button Peter Crouch pressed so spectacularly with his early red card in Madrid. Spurs knew only an early goal would provide them with the faintest hope of somehow turning around Real's advantage from the first leg, but Mourinho's men were resolute and their only moments of serious anxiety came from three penalty claims. Gareth Bale went down far too easily with Alonso in close attendance and Italian referee Nicola Rizzi was right to ignore the appeals.
A second incident involving the former Liverpool midfield man, this time as he challenged Modric, was a much closer call and Real were fortunate to get the benefit of the official's doubt.
The frustration continued as Roman Pavlyuchenko was involved in another collision in the box with Real defender Raul Albiol but once again there was no response from Rizzi.
Pavlyuchenko had Spurs' best opportunity of the first half when Aaron Lennon found himself unmarked 12 yards out, only for the Russian to sky his attempt well over the top. He also tested Iker Casillas with a long-range effort that was held comfortably by the Real keeper.
The Spanish side's responses were fleeting but their main business was closing out the tie with no alarms.
They did suffer one setback, however, when Ricardo Carvalho was booked for a foul on Tom Huddlestone that means the influential former Chelsea defender misses the first leg of the semi-final against Barcelona.
Spurs were threatened when Sergio Ramos met Mesut Ozil's corner, only to see his header turned away by Gomes.
The brutal truth was that the game was up after those 90 harrowing minutes in Madrid but any lingering hope Spurs had of provoking an unlikely collapse from Real was snuffed out in one dreadful moment for Gomes.
Ronaldo's effort from 25 yards travelled more in hope than expectation but the Brazilian fumbled hopelessly and even botched his attempt to recover the situation as the ball crept over the line.
It was then all about limiting the damage and clawing back a measure of respectability for Spurs and Pavlyuchenko had a chance to at least draw them level on the night but he headed Lennon's cross over the top when unmarked.
Lennon was then withdrawn by Spurs and replaced by Jermain Defoe, who wasted no time in testing Casillas with a low 20-yard effort that he turned away.
Spurs, to their credit, continued to battle and almost scored when Casillas misjudged Rafael van der Vaart's corner and Defoe almost smuggled home the loose ball.
Tottenham left themselves with an insurmountable task after the first leg and now must focus their attention fully on the Premier League.
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