Harry Kane says a top-four Premier League finish will not make Tottenham's season a success, admitting Spurs are "lacking something" as speculation over Antonio Conte's future grows. 

Spurs have seen their hopes of avoiding another trophyless season evaporate within the space of a week, following up an FA Cup loss at Sheffield United with a Champions League exit against Milan.

Tottenham suffered a dire Premier League defeat at Wolves between those two eliminations, and they have now failed to score in three successive games for the first time since a three-match losing run in April and May 2019.

With Spurs now facing a battle for a top-four berth, Kane says a 15th consecutive campaign without silverware is unacceptable.

"Where we're at as a club, we should be winning trophies," Kane told reporters. "The top four [being Spurs' only target] is a consequence of not playing as well as we want to play. 

"For sure, it's not enough for this club. I totally understand the fans' frustrations. Top four is not good enough for anyone at this club, especially the fans. They have the right to voice their opinion.

"The last week especially just hasn't been good enough. Before the Sheffield United game, the season could have been a whole lot different. 

"You go through there, you take that momentum into the league game and this game [against Milan]. 

"But I feel like that loss last week put a dagger in our hearts and as you can see, we haven't really recovered from that."

Spurs' expected goals over two legs in a 1-0 aggregate defeat to Milan was only 0.91, and they have failed to win any of their past five Champions League knockout games (D1 L4) since beating Ajax 3-2 at the semi-final stage in 2019.

It has been suggested their latest failure could spell the end of head coach Conte's tenure at the club, with the Italian accepting Spurs may sack him before his contract expires at the end of the season.

Asked for his thoughts on Conte's future, Kane said: "It's his decision, he's going to be the one that makes that choice. 

"All we can do as players is try to perform for him, work as hard as we can. That's what we're doing. You can't fault the effort of the players. We're just lacking something. 

"We've talked about mentality before and that ruthless hunger to be better, to be the best, to be one of the best teams in Europe. We just haven't quite found that yet."

Son Heung-min has been backed to rediscover his best form by incoming South Korea coach Jurgen Klinsmann, who believes a difficult situation at Tottenham has hampered the attacker.

Son has endured a poor season with Spurs, scoring just five Premier League goals after sharing the Golden Boot with Mohamed Salah last term, and his troubles have carried onto the international stage.

The forward wore a protective mask at last year's World Cup after suffering a fractured eye socket ahead of the tournament, where he failed to net in four appearances.

Son produced another ineffective performance as Spurs exited the Champions League against Milan on Wednesday, leaving the future of boss Antonio Conte in serious doubt.

His new international coach, however, retains faith in Son's ability to bounce back, saying: "I'm a big fan of Sonny. There's no doubt. He had a very difficult World Cup because he was not 100 per cent healthy.

"Obviously I saw all the games and I felt for him, but I think this is a normal period and every player goes through little up and downs. Also, the situation at Tottenham is sometimes not so easy. 

"I hope that I'm going to see him in two weeks and he comes with a smile and is hungry for the national team."

Klinsmann was named as Paulo Bento's successor last month, with the Portuguese coach stepping down after a 4-1 defeat to Brazil in the last 16 at the World Cup.

Asked how he would approach the role at his unveiling on Thursday, the former Germany international said: "Obviously, my personal background was a striker, so I always love to attack, and that means I’d rather win a game 4-3 than 1-0. 

"But at the end of the day, I think a coach always has to adapt his approach and his philosophy to the people around him, mainly the players. 

"So based on who you have as players and what capabilities your team has, you need to adapt that philosophy to your approach."

South Korea will face South American opposition in their first two outings under Klinsmann, with Colombia and Uruguay their opponents for friendlies later this month.