Tottenham Hotspur secured a deserved win - their first under Igor Tudor - against Atletico Madrid but failed in their attempt to overturn a three-goal deficit as they went out of the Champions League in the last-16 stage.

Spurs were left with too much to do after a calamitous 5-2 first-leg defeat in Madrid - one of four in five matches since Tudor replaced Thomas Frank as manager.

But their latest improved performance - following a 1-1 draw at Liverpool - in a thrilling return leg will offer encouragement as they now turn to their main priority of avoiding relegation from the Premier League.

Spurs needed the first goal on the night, starting well and making the breakthrough on the half-hour mark when Randal Kolo Muani headed home an inviting cross from Mathys Tel on the right for his fourth goal in this season's competition.

French forward Tel then had a golden chance to set nerves jangling for their opponents when he broke through, but visiting keeper Juan Musso - a replacement for the injured Jan Oblak - made a crucial block.

Guglielmo Vicario did the same at the other end to deny both Julian Alvarez and Giuliano Simeone.

But Atleti punctured the atmosphere two minutes after the restart when former Manchester City forward Alvarez beat the Spurs keeper with a superb strike into the top corner.

Spurs were furious, insisting Xavi Simons had been fouled in the build-up by the Argentine, who then led a brisk counter-attack and finished off Ademola Lookman's pass.

But Dutch forward Simons exacted swift revenge by putting his side in front again with a fine curling low drive five minutes later.

Diego Simeone's men were hanging on and thankful to Argentine Musso, who made vital stops from Pedro Porro and Radu Dragusin as Spurs tried to set up a grandstand finish.

The importance of those saves was emphasised when the Spanish side snuffed out any remaining hopes of a comeback with 15 minutes left as David Hancko headed in at the near post from an Alvarez corner.

Atleti were finally able to breathe easily as they set up a last-eight meeting with Barcelona, although Simons' late penalty - following a foul on him by Jose Maria Gimenez - gave the hosts the victory they deserved on the night.

Spurs will now turn their attention to the crucial league meeting with fellow strugglers Nottingham Forest at home on Sunday in the battle to beat the drop.

Spurs were always fighting against the odds after that desperate first leg in Madrid put Atletico in complete control of this tie.

But, despite their recent struggles, Tudor's side actually offered up moments of hope as they were willed on by home fans who appreciated the effort and refusal to give up despite a mammoth task.

And this display, coming on top of a deserved league draw at Liverpool on Sunday, drew warm applause at the final whistle despite the disappointment of an exit from the competition.

Spurs deserved their success on the night, showing enough to offer real encouragement as they now tackle the main business of their season - namely staying in the top flight.

And they be positive going into Sunday's all-important home meeting with Forest, who are only one point behind them in the table along with third-bottom West Ham.

The big opportunity for a miraculous comeback perhaps came when Tel missed a huge chance to make it 2-0 late in the first half, but he was also one of his side's standout players, a threat throughout.

And what will also give Spurs and Tudor added belief was the manner in which they responded to the setbacks of Atletico's two goals, pushing until the final whistle.

They never gave up, despite the almost certainty of defeat to earn a morale-boosting victory.

It was a far cry from the last time they were here, feeling the full wrath of their own fans after a dismal Premier League defeat by Crystal Palace.

There was genuine appreciation for Spurs' efforts - and that alone will help fuel their battle for survival if they can continue to build on the improvement in their last two games.

Spurs host fellow strugglers Nottingham Forest in a crunch Premier League meeting on Sunday, 22 March (14:15 GMT).

Atletico Madrid visit neighbours Real Madrid in La Liga on Sunday (20:00 GMT).