It was not so much the old line about it being a bad time to concede, even though it plainly was. It was more the sense of inevitability. Everyone could feel that Manchester City were going to score, to reduce Tottenham’s 2-0 lead before the interval in Wednesday’s Carabao Cup last-16 tie at Spurs’s stadium.

City had shaken their heads clear and from the 35th minute they pushed hard, creating openings. Spurs dropped back. They were increasingly loose. They walked into trouble. The collective “aaah” from the home crowd when four additional minutes were signalled said it all. They wanted the half-time whistle. So did the manager, Ange Postecoglou. We were into the fourth of them when Matheus Nunes scored for 2-1.

Postecoglou shook his head. He had spoken on Tuesday about how his team were “struggling in difficult moments” because they “lack some maturity and leadership”. The absence of authority as City got themselves back into the game was stark and alarming. Now it truly was a difficult moment.

Spurs had won seven of their previous nine matches in all competitions and yet the two that got away seemed to have had the greater impact on the climate around the club. There was the 1-0 loss at Crystal Palace on Sunday, the worst performance of the season. And the 3-2 defeat at Brighton at the start of October, when a 2-0 half-time lead was extravagantly frittered away. As Spurs headed for the dressing room, the prospect of a repeat was real.

“I am very angry that we conceded the goal in the last second – we can’t do that,” the midfielder Dejan Kulusevksi said. “It changes everything when you’re going to go in at half-time at 2-0 and then it’s 2-1.”

Postecoglou knows his team will mature and develop leadership skills only by confronting adversity. The alternative of the club signing experienced players with such qualities (probably for big fees) is not a part of the project. And so it was no exaggeration to describe half-time against City as a pivotal juncture.

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“We were, of course, angry,” Kulusevski said. “But people said: ‘Listen, we are winning 2-1, keep going.’ The manager said we had to keep playing our way – don’t defend too deep, keep pressing.”

Spurs found new energy. They rediscovered their thrust, creating a fistful of chances before the hour. Now came a different problem to stress their fans, Postecoglou, too – profligacy. Timo Werner had scored the opener but he was the biggest culprit. Even Kulusevski, outstanding in the No 10 role, could not finish when one-on-one with Stefan Ortega.

It felt as if the whole game was an internal struggle for Spurs, a battle to break down barriers. Again, the nerves jangled as the end approached. Again, it felt inevitable that City would at least have the chance to equalise. They did when Guglielmo Vicario flapped at an 88th-minute corner and the ball broke for Nico O’Reilly, whose shot was goalbound only for the substitute Yves Bissouma to clear off the line.

Had O’Reilly scored and City won on penalties, Spurs would still be kicking themselves because they were the better team; there was plenty for Postecoglou to like. We all know how the story would have been told if they had been unhinged. But they got it over the line to set up a home quarter-final against Manchester United and it was surely a result to bolster the belief, to bring stability in the face of the edginess.

“Yeah, but it should not be like that – we don’t want to be up and down,” Kulusevski said. “If you want to be a champion you have to be there every game. That’s the main part that everyone has to understand.”

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Kulusevski was certainly up for it against City. He always is. The 24-year-old, for example, has scored in all three of his away games against them. “I take it personally to play against City,” he said. “I love to play against the best … it’s just extra motivating.

“It’s a personal thing. Everybody that’s close to me knows it. I had prepared for this game for a long time. I had it in my head for a long time. There’s no fear; it’s the complete opposite of fear. I knew I had to perform and I did.”

Where Spurs have struggled, Kulusevski says, is away from home against the deeper-sitting, more physical teams. Such as Palace, perhaps. There is a related question mark against how Postecoglou sets up his midfield.

Kulusevski has embraced his central attacking role to such an extent this season that he has to play there. But Postecoglou must also accommodate James Maddison. When he started both at Palace, with Bissouma as the holding player, it did not go well. There is an argument that Spurs could be better calibrated in a 4-2-3-1 with two from Bissouma, Pape Sarr and Rodrigo Bentancur in front of the defence.

“We have to improve away from home against teams that play very physical and don’t play the football that was played in the City game,” Kulusevski said. “I’m not afraid of these games [against City] but I know we have to improve a lot in these away games.

“We have to speak a lot about that in the team. We have to change some things when we play against the teams that play more difficult football. Did we discuss this after the Palace game? No, as we had to focus on City. But I would like to speak about it in the future.”