For Tottenham Hotspur it is not going to be easy to find a way back. They will still like to think they can save themselves and, to give them their due, they can be emboldened by the memories of that epic night against Manchester City which got them this far. Yet it will clearly need something dramatic again – something, frankly, that looked beyond them for long parts of this defeat – if they are to stop this vibrant Ajax side reaching the final.

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What other conclusion can be drawn after that 30-minute period in the first half when Ajax seemed utterly determined to remind the watching world that they own the patent to Total Football? In those moments Ajax demonstrated to Spurs how demanding the Champions League can be at its elite level, when the quality suddenly goes up a few notches and opponents are passing the ball as they would on a computer game. And for a while, with Donny van de Beek scoring one goal and threatening others, it did look as though Ajax genuinely fancied their chances of making sure the second leg was a formality.

As it turned out, Spurs made it through a difficult night without conceding again and can at least be encouraged by the improvement in their second-half performance. It was still a deflating night for the Premier League’s third-placed side, trying to reach their first European Cup final, but they will also know it could have been significantly worse when they recall how close Ajax came to doubling the lead in the 78th minute. The shot from David Neres thudded back off a post and Spurs, saved by the woodwork, can cling to the hope that all sorts of possibilities remain open in the Johan Cruyff Arena on Wednesday week.

Facebook Twitter Pinterest Donny van de Beek sidefoots his finish past Hugo Lloris to give Ajax a precious away goal at Tottenham. Photograph: Tom Jenkins/The Guardian

By then they will have Son Heung-min available again, having missed this match because of the number of bookings he had accumulated under Uefa’s totting-up system. Yet Harry Kane will still be out because of his damaged ankle ligaments. Spurs are determined to show they can flourish without the England captain but it was difficult to leave the stadium without thinking Kane’s absence was a considerable factor in why they could not create more penalty-box danger. Hard as Fernando Llorente tried there was not one occasion when Spurs created what could be described accurately as a clear scoring opportunity.

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Ajax, on the other hand, had three of them, plus a selection of other reasonably inviting chances to threaten the Spurs goal, and moved the ball so elegantly and purposefully at times it must have been startling for the home supporters to see their team being so comprehensively outplayed.

Not that it should have come as any surprise that Erik ten Hag’s side were so ambitious in possession. What we saw here was merely Ajax continuing where they had left off against Juventus in the quarter-final and, before that, Real Madrid in the first knockout phase. It was glorious to watch, slick and inventive, with an emphasis on speed, control and football intelligence.

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Ajax have shown already why they have serious aspirations of adding to their three successive European Cups from the 1970s, as well as the one they won in 1995, and they were quick to reinforce that point. Around the half-hour mark there was one statistic to show the away side had had 69% of the ball. In truth, that seemed generous on Spurs.

Underpinning everything was the intensity of how Ajax played, their immense work-rate and refusal to wilt even when Spurs were trying to put them under pressure in the second half. As has been apparent this season Ajax understand the merits of scoring in the away leg. They managed two in Turin, to go with the four they scored in the Bernabéu, and right from the start they seemed determined to go for it again.

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Spurs could not get near the ball and Danny Rose was marginally out of position when Hakim Ziyech played the killer pass for the 15th-minute breakthrough. Van de Beek controlled the ball while swivelling to face the goal all in one movement. That left him in front of Hugo Lloris and the goalkeeper was fooled by the way the Ajax player shaped to shoot. It was a brilliant deception. Van de Beek waited for Lloris to go down and then drew back his right foot for a second time to pick out the bottom corner.

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When everyone gets time to catch their breath the Spurs fans should reflect this was exactly the kind of occasion for which the stadium was built. It was smart of them to stop the music a few minutes before kick-off to let the supporters create their own atmosphere. The noise was unrelenting and, if nothing else, at least Spurs can realistically think they are still in with a fighting chance.

As well as Neres striking a post, Ajax will also reflect on another opening earlier in the match when Van de Beek dummied the ball then ran on to Dusan Tadic’s pass to give himself another shooting opportunity. This time Lloris saved his team.

Spurs found the first half tough, to say the least and there will have to be questions about the decision to send Jan Vertonghen back on after the clash of heads with Toby Alderweireld that eventually ended his involvement. Vertonghen was bloodied in the collision and so wobbly on his feet the Spanish referee was among those questioning whether the player should stay on. Spurs decided he should continue after he had been examined by their medical staff but Vertonghen was obviously in a bad way and it became clear shortly afterwards that it had been a bad idea. For Spurs it was a bruising night all round.