Diego Simeone's side trailed three times in north London but they did just enough to go through 7-5 on aggregate.

Randal Kolo Muani put Tottenham ahead in the first half before Julian Alvarez levelled immediately after the break.

Xavi Simons netted to give spirited Tottenham a glimmer of hope, but David Hancko's equaliser extinguished any chance of an incredible comeback.

Simons' stoppage-time penalty came too late for Tottenham to complete their mission impossible.

Atletico will meet Barcelona in the last eight after their Spanish rivals crushed Newcastle 7-2 on Wednesday.

Third-placed Atletico, who recently knocked Barca out of the Copa del Rey, are 13 points behind Hansi Flick's La Liga leaders.

Simeone's men will have to improve significantly on this erratic display if they are to reach the semi-finals.

Languishing in 16th place in the Premier League, Tottenham's European exit leaves them to focus on their bid to avoid the humiliation of relegation.

Igor Tudor's men are just one point above the relegation zone as they teeter on the brink of playing in the second tier for the first time since 1977-78.

Bolstered by their first win since interim boss Tudor replaced the sacked Thomas Frank, Tottenham host fourth-bottom Nottingham Forest on Sunday in a crucial clash in their fight for survival.

Tottenham defender Micky van de Ven this week insisted any reports of players not caring about the club's precarious situation were nonsense.

Van de Ven slammed suggestions the players have "checked out" and their determined attempt to rattle Atletico suggested Tudor has kept them motivated in the midst of their turbulent run.

Tottenham were 4-0 down in 22 minutes in the first leg in Madrid last week, with Tudor hauling off keeper Antonin Kinsky after just 17 minutes following a pair of errors that led to goals.

- Atletico survive -

They competed far more gamely this time and Mathys Tel forced an early save from Atletico keeper Juan Musso, who was deputising for the injured Jan Oblak.

Tel carried the greatest threat for Tottenham and his near-post drive was parried away by Musso.

Unsure how to approach a tie that looked over before they even arrived in London, Atletico struggled to find any rhythm for long periods.

Tottenham's pressure was rewarded in the 30th minute when Tel lofted a superb cross toward Kolo Muani and the French striker punished sloppy marking to power his header past Musso from 10 yards.

Tel should have pulled Tottenham even closer, but his close-range shot was straight at Musso.

Atletico barely threatened until Alvarez's long-range blast hit the crossbar just before half-time, but they drew level two minutes after the interval.

Tottenham appealed in vain for a foul on Simons and Atletico surged forward, with Ademola Lookman picking out Alvarez for a nimble shot on the turn that flashed past Vicario from 12 yards.

To their credit, Tudor's team didn't surrender and Simons struck five minutes later.

Archie Gray scythed through the Atletico midfield, setting up Simons on the edge of the area for a brilliant strike that arrowed into the far corner.

Tottenham scented a miraculous escape and Musso had to make a brilliant save to repel Pedro Porro's strike before scrambling away another effort from the defender.

Hancko levelled in the 75th minute, getting in front of Gray to head home from Alvarez's corner.

Fouled by Jose Maria Gimenez, Simons slotted home from the spot in the final minutes, but Atletico survived a tense finale.