Perhaps the greatest compliment that can be paid to Leicester City is that it was difficult to remember the last time a team have gone out of Europe and earned this kind of ovation. It has been an epic run, they have had some great fun along the way and they will cherish the memories but ultimately the applause at the final whistle was for the end of the adventure.

They gave everything they could and, if nothing else, Leicester reminded us of all their better qualities during that period of concerted second-half pressure when they genuinely seemed to believe themselves capable of pulling off an almost implausible feat of escapology.

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Atlético Madrid will have a better understanding now why Leicester won the Premier League last season and it was rare to see Diego Simeone’s players looking as hassled as they did once Jamie Vardy had changed the complexion of the night with a goal just after the hour.

The problem for Leicester was that they needed three goals at that point because of the header from Saúl Ñíguez that gave Atlético a first-half lead, 2-0 on aggregate and the considerable advantage of an away goal.

Craig Shakespeare’s tactical changes at half-time, going for all-out attack with a three-man forward line, had a dramatic impact and what a grandstand finish it would have been if Vardy’s next chance, seven minutes after scoring, had not ricocheted off a defender’s legs. Leicester fought to the end and at the final whistle there was something symbolic about the way Simeone made it his business to approach every single player in blue and shake his hand.

In the end, though, the joy of reaching the semi-finals belonged to the side going for their third final in the past four seasons. The only team to have got the better of Atlético in this competition during that time is Real Madrid and perhaps in hindsight Leicester will reflect it was a mistake to operate with so much restraint in the first leg.

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It is hypothetical now but what a difference it might have made if they had conjured up an away goal in the Estadio Vicente Calderón. Instead they could not even manage a solitary attempt on target – or in the case of Vardy a single pass – and their failure to score in Madrid always left them vulnerable to the possibility that their opponents might get one in the return leg.

All of which meant Saúl’s expertly taken goal, 26 minutes in, put Leicester in the unenviable position of knowing they would need to score three. And no side have done that against Atlético in this competition since they lost at Olympiakos in September 2014, a run now spanning 33 matches. Leicester always needed something special but the goal left Atlético in a position of strength they were never likely to relinquish.

Facebook Twitter Pinterest Kasper Schmeichel cannot keep out a brilliantly guided header from Saúl Ñíguez’s, far left. Photograph: Ben Stansall/AFP/Getty Images

Shakespeare responded at half-time by bringing on Leonardo Ulloa and Ben Chilwell in place of Yohan Benalouane and Shinji Okazaki and becoming the latest Premier League manager to experiment with a three-man defence. The new 3-4-3 system was both bold and necessary and Atlético, streetwise though they are, seemed taken aback by the refusal of their opponents to accept their fate.

Chilwell and Marc Albrighton took on the wing-back roles while Mahrez moved alongside Ulloa and Vardy into a new-look forward line and almost immediately Leicester had a more threatening edge.Mahrez, in particular, seemed invigorated while Ulloa’s presence gave Leicester a target for their high balls. Vardy clipped in the equaliser after Chilwell’s deflected shot had spun conveniently into his path and it was just a pity from Leicester’s perspective that Stefan Savic managed to block the striker’s next attempt. If that had gone in, Leicester would have had all the momentum to go for another one.

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At the same time there was no doubt over the two legs that the better side got through. Leicester put in a commendable effort once their situation became desperate but, overall, they would not have scored highly if points were awarded for wit, creativity or refinement. Too many passes were misplaced and in the first half there were only brief flashes of danger from Vardy and Mahrez.

Mahrez was also partly culpable for Saúl’s goal bearing in mind his half‑hearted attempt to close down Filipe Luís before Atletico’s left-back swung over the cross. Saúl eluded Albrighton and Christian Fuchs before making the decisive connection.

His neck muscles were strained, the cross thudded back off his forehead and the ball was still picking up speed as it bounced past Kasper Schmeichel. As headers go, it could hardly have been executed more stylishly.

Leicester had to gamble and Simeone, effusive in his praise of Leicester’s display, credited Shakespeare afterwards for the tactical switches that threatened La Liga’s third-placed team. Wes Morgan, rushed back after six games absent with a back problem, eventually succumbed to a hamstring injury and Schmeichel spent stoppage time in the opposition half. Leicester needed two goals and had only four minutes. Yet, typically, they still went looking for that final, elusive glory.