Spurs were unable to produce the miracle required to overcome Real as they exited the competition with a quarter-final second leg defeat thanks to Heurelho Gomes' second-half clanger.
Gomes has been a pillar of the club's domestic and European campaigns this year, but his failure to hang on to Cristiano Ronaldo's routine 30-yard drive ensured that any chance Spurs had of coming back from the four-goal deficit they accrued in the Bernabeu were over in the 50th minute.
Spurs threw everything they had at their highly-decorated opponents in the first half and had two convincing penalty appeals turned down.
Gareth Bale, Aaron Lennon and Roman Pavlyuchenko all excelled, but their efforts were not enough to give Spurs fans one more memorable night to add to their collection this year and Madrid and Jose Mourinho will now get the chance to prove they are Europe's best as they take on Barcelona in the last four.
The defeat brought to and end a dream debut season in the Champions League in which Tottenham have won the hearts of many a neutral thanks to the enterprising football which had seen them tear apart Inter Milan and brush past their neighbours AC Milan to make the last eight.
Rarely has a team making their first appearance in the Champions League had such a successful bow, and should they qualify for next year's tournament, they will be confident of mixing it with Europe's giants again.
There will, however, be a nagging thought at the back of Harry Redknapp's mind that his team could have had the better of the nine-time champions had it not been for Peter Crouch's reckless first-leg dismissal and Gomes' error in tonight's second leg.
Footage of Bale's hat-trick in the club's 4-3 defeat against Inter Milan greeted their supporters as they took their seats looking for their team to give them another historic European night.
The three goals the Welshman fired in at the San Siro would not be enough to even take this tie to extra-time though after last week's 4-0 hammering at the Bernabeu.
Mourinho warned that his team had come to London to score and they looked as if they meant business early on, with Ronaldo, Mesut Ozil and first leg hero Emmanuel Adebayor all probing the Tottenham backline.
Spurs looked equally intent on breaking the deadlock though and Bale thought he should have had a penalty in the fourth minute as he skipped by Xabi Alonso and fell to the ground. Referee Nicola Rizzoli waved play on and replays suggested he was right to do so.
Four minutes later and Alonso clipped Luka Modric in the box. The Italian referee once again denied the home side a spot-kick despite the claim looking to be legitimate.
The pace of Bale and Lennon caused Madrid problems, with Sergio Ramos and Marcelo both found floundering in the early exchanges.
The home crowd urged their side on, but Ronaldo reminded them of the threat he posed as he danced past his marker before firing wide after 20 minutes.
At the other end, Rafael van der Vaart executed a brilliant turn to unleash Lennon down the right. His pass found Pavlyuchenko but he blazed over to waste a great opportunity to break the deadlock.
The Russian made amends by gaining an inch on Raul Albiol moments later only to be tripped by the defender in the box. The referee waved play on and Spurs were denied yet another spot-kick, much to the home fans' anger.
Tottenham thought they had the goal they craved just before half-time but Modric was correctly ruled offside after he had headed back to Bale, who smashed home into the net.
The tie was effectively over in the fifth minute of the second half when Gomes let Ronaldo's 30-yard drive slip through his fingers. The Brazilian swivelled and tried to claw the ball away before it crossed the line but the damage had already been done. Any slim hopes Spurs harboured of salvaging the tie were gone.
Redknapp brought Jermain Defoe on for Lennon and he almost scored within moments of taking the pitch, drawing a good diving save from Iker Casillas.
The fierce atmosphere that had been prevalent before the opener had disappeared after Gomes' error, but the keeper did well to keep out Kaka in the 65th minute after the Brazilian had come on for Ronaldo.
The chants of "we're gonna win 6-1" showed the Tottenham fans still had faith and they almost equalised when Defoe's strike was blocked by Casillas from just two yards out.
Sandro collapsed inside the Madrid box under pressure from Alvaro Arbeloa as Spurs' bid for an equaliser continued but with substitutes Karim Benzema and Kaka in full flight down the other end, the hosts were in danger of slipping further behind.
Marcelo almost made it 2-0 when his audacious chip landed on top of Gomes' goal as the clock ticked towards 90 minutes.
Van der Vaart attempted to curl a 20-yard strike in against his old club with five minutes left, but Casillas watched his effort sail over the bar.
Bale then drifted past his marker to lay off to Defoe in injury time but a block denied Spurs the equaliser they were searching so desperately for.