There were boos from the Tottenham support at half-time and sighs when Cristian Romero got himself sent off for a second wild lunge on 77 minutes. There were more jeers when Antonio Conte substituted Dejan Kulusevski and jettisoned his brief flirtation with a line of four attackers. On came Davinson Sánchez in a role that nobody seemed to be able to describe.

And it all led up to the inevitable outpouring at full time, the loudest jeers of the night from a home crowd that wanted to believe but in their hearts knew that this team, set up by this manager, was never going find a way.

Perhaps the slender scoreline made it worse. Tottenham always had a puncher’s chance, even one with jelly legs and double vision, against a Milan team which lags fifth in Serie A, in the throes of a disastrous title defence; one outplayed both home and away by Chelsea at the group stage of this competition.

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In the 65th minute, Pierre-Emile Højbjerg ran from right to left for Spurs, kept on going and banged a shot towards the near, top corner, which forced the Milan goalkeeper, Mike Maignan, to tip over the crossbar. It was indisputably the first time that the home fans were seriously stirred. And pretty much the last.

Harry Kane almost bailed them out in stoppage-time – of course he did – heading goalwards from a Son Heung-min free-kick and watching Maignan make a fine save. But the bigger takeaway from the six extra minutes was the sight of hundreds of supporters streaming for the exits. They did not know what would flash up on the big screen at full time – a message that the Victoria Line had melted down. Two words. Tin and lid.

It was not a night for any Spurs hard-luck stories because they were well beaten, rather for introspection and questions that hung heavy in the air. How can Kane, who is out of contract in June 2024, stick around for more of this? Also, whither Conte?

The manager, who was back in the dugout after his well-documented health problems, has refused to say whether he will remain at the club for another season. Given how the life has seeped out of his tenure, flatness and half-empty glasses the motifs now, it is questionable how hard the club would fight to keep him. Conte has won only one Champions League knockout tie as a manager in six seasons of trying.

The Spurs crowd wanted a fast start, much like the one that Milan had made in the first leg when Brahim Díaz scored after seven minutes. But this Conte team is not really set up to blow the bloody doors off – especially against opponents who are comfortable on the ball and in their shape.

It was Milan who eased into the tie, Spurs looking rigid; edgy, too, as evidenced by Romero’s first yellow card on 17 minutes – a reckless jump into Rafael Leão. That would have seen him suspended for the quarter-final had Spurs progressed. Clément Lenglet would suffer the same fate when he caught Olivier Giroud with his arm in an aerial challenge, albeit it was a harsher decision.

Stefano Pioli has recently switched to a back three and there was flexibility about the Milan system; Díaz roaming from the right to the No 10 role and back, Leão going where the mood took him. The wing-backs, Junior Messias and Théo Hernandez, pushed high and it was the former who should have opened the scoring.

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Milan worked a short free-kick routine after the Romero yellow card with Sandro Tonali playing the killer pass for Messias. Ben Davies had gambled on the interception and lost. Messias was in on the right-hand side only to drag wastefully past the far post.

The first half was a tough watch from a Spurs point of view. The errors on the ball were pronounced, ditto the hesitancy. Conte wanted to counterattack but apart from one early surge by Kane, which led to an Emerson Royal shot that was blocked, Milan were never going to let that happen. Spurs were so static and predictable. It was still remarkable to hear the smattering of boos at half-time.

Milan were much slicker, especially Díaz and Tonali, partly because Spurs did not bring any sort of press. The gulf between Milan’s composure and the home team’s telegraphed patterns was jarring.

There had been drama before kick-off, the north London roads jammed, leaving the team buses to inch along. Would they make it on time? It felt touch-and-go. Spurs would finally punch in at 7pm, Milan five minutes later. The kick-off was set back by 10 minutes.

But there was little excitement on the pitch, the atmosphere failing to crackle up to and including the interval when the former Spurs captain, Steve Perryman, took a long trudge down memory lane as the special guest.

Conte’s introduction of Pedro Porro injected a bit of energy and there was the sense, perhaps just a hope, that Spurs were gearing up for a grandstand finish when Højbjerg extended Maignan. That said, Milan continued to threaten. Díaz had extended Fraser Forster on 52 minutes. Giroud would go close after a move involving Leão and Díaz.

Enter Romero, who can never be accused of holding back in the 50-50s. He was late, however, on Hernandez on the right flank, injuring himself in the process and limping off when the referee, Clément Turpin, showed him the red card. Turpin had given the yellow straight away. The delay before the red was almost comical.

Conte had sent on Richarlison and switched to 4-2-4. Now he withdrew Kulusevski and how the crowd howled. Tonali had a shot blocked when well-placed and, after Kane’s late chance, the substitute, Divock Origi, hit the post at the other end. For everybody connected to Spurs, it was a night to forget.