Fernando Llorente has described Harry Kane as “one of the best strikers in the world – if not the best”. The Spain World Cup winner, who joined Tottenham Hotspur from Swansea City on transfer deadline day, has now seen Kane’s quality at first hand and he believes the 24-year-old has it all.

Llorente made his Tottenham debut on Wednesday night as an 87th-minute substitute for Kane in the 3-1 Champions League win over Borussia Dortmund at Wembley. It was the latest game in which Kane had played a starring role. His two goals were the headline detail of a remorseless performance and Llorente led the applause as he came off.

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“I think he’s awesome,” Llorente said. “He’s one of the best strikers in the world, if not the best. In front of goal, he’s lethal. The truth is that he is in a sweet moment, and we have to make the best of that. He gives us so much. He’s an extremely complete player; he doesn’t just score. In every aspect, he’s very complete.”

Llorente revealed that he joined Tottenham instead of Chelsea after the club’s manager, Mauricio Pochettino, made a “last-minute” personal phone call to him. Chelsea had tracked Llorente for much of last season and they made an unsuccessful attempt to sign him from Swansea in January. Llorente had previously played under the Chelsea manager, Antonio Conte, at Juventus but he also goes back with Pochettino.

Llorente made his professional debut for Athletic Bilbao in 2005 against an Espanyol team that featured Pochettino in its defence and he would face him again after Pochettino became the Espanyol manager.

“The truth is that Chelsea have been after me for a long time but, at the end, you know how this works,” Llorente said. “At the very last minute, Pochettino called me and convinced me [to join Tottenham]. The Tottenham project is impressive. They have done very well in the last few years and I think I fit very well with this project. I think I can help them a lot.

“It is clear that Pochettino played a very important role in my decision. I have known him since he was playing in Spain. There is even a nice anecdote because I made my first-team debut against him. He was at the end of his playing career and I was at the beginning of mine. Then, he was the Espanyol manager and I faced him several more times. Now, I play under him at Tottenham and I really want to give my best. I’m very happy because, at the end, everything came out perfect.”

Toby Alderweireld felt that Tottenham showed a new-found tactical maturity against Dortmund and he emphasised the point with a snappy soundbite. “We didn’t play like children,” the central defender said. “We played like adults.”

Tottenham’s priority in home matches is to squeeze high up the pitch and impose their pressing game but against opposition of Dortmund’s class, there was the realisation that they would have to play in a more containing and reactive way, which featured clinical thrusts on the counterattack.

Dortmund hogged the ball and they were easy on the eye, particularly in the first half, when they stretched Tottenham. During that period, Pochettino’s team sat too deep and they invited Dortmund on to them too much. They would push up more in the second half and find a better balance. And yet Dortmund still trailed 2-1 at the interval.

The story of the evening from a Dortmund point of view was heavy on hard luck. They could lament the goal that Pierre-Emerick Aubameyang had wrongly ruled out for offside in the 56th minute – which would have made it 2-2 – and argue that Kane ought to have been penalised for a foul on Nuri Sahin in the buildup to his first goal for 2-1.

Moreover, Dortmund made the game; they looked high-end and sophisticated, and they threatened. On the other hand, there was naivety from them at the back and the goalkeeper, Roman Burki, was twice beaten at his near post.

Facebook Twitter Pinterest Toby Alderweireld celebrates at the final whistle. Photograph: PPAUK/Rex Shutterstock

Alderweireld was impressed at how Tottenham dug in during the first-half while making their two counter-attacks pay – in the shape of goals for Son Heung-min and Kane. They were forced to defend manfully but they did so and Alderweireld could enjoy how they were able to come out more in the second half, when Kane added his second.

It was a triumph for Tottenham’s game management and it certainly felt that they had learned a few lessons from last season’s failed Champions League campaign, when they were outmanoeuvred at Wembley by Monaco and Bayer Leverkusen.

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“It wasn’t going our way but we fought, we kept compact and we tried to be dangerous when we came out,” Alderweireld said. “We did that in the first half and the second half was better. We’ve learned quick and we have to learn quick. It’s a good step from last season and a good start.

“When it doesn’t go our way, because we want to press and sometimes we’re a little bit late, we [have to] just stay compact to get through it. And when we got the ball, we tried to be dangerous. That’s a big plus from last season. They had a lot of possession but we defended very well. We didn’t give a lot of chances away. In the second-half, Dortmund got more tired and we should have scored more.

“Everybody knew what we had to do. We have more experienced players and they know what to do now in those kind of situations. They keep their heads calm and bring what they have to bring. We’ve learnt from last season.”

Kane was pleased at how Tottenham were “clinical when we needed to be” but he also made the point that they could not hope to press all the time against the top teams in Europe. The buzzwords have to be balance and savvy.

“It was an experienced performance from us,” Kane said. “We were clever in the way we pressed and when we dropped off. We’ve got to learn we can’t always press 100% against good teams because they’ll find spaces. We dropped off when we needed to and we caught them on the counterattack with the spaces in behind. We learned from last year’s campaign. We said we wanted to improve our home form and we’ve done that.”

The blot was the stoppage-time sending-off of Jan Vertonghen for a second yellow card. He threw an arm back and caught Mario Götze, seemingly accidentally, and saw the Dortmund substitute go down theatrically. Vertonghen, who will be suspended for the trip to Apoel Nicosia, made it plain that he was unimpressed at Götze.

“I didn’t agree with it,” Vertonghen said. “I had no intention of hitting him. For me, it was a mistake. I was trying to win the ball, protect it, but I had no intention to hit him. I think a couple of guys made too much of it.”