Jan Vertonghen has said it would be a “big shame” if Tottenham’s current generation of players do not win a trophy.

Spurs travel to Crystal Palace on Sunday for a FA Cup fourth-round tie that has increased in significance following their Carabao Cup semi-final loss to Chelsea. The FA Cup is by some distance their most realistic means of ending a trophy drought that stretches back 11 years.

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“It’s very important,” said Vertonghen of the tournament. “This team deserves so much more, so many trophies. Over the last five years, we haven’t had a lot of luck. We’ve been so good. It would be a big shame if we don’t reward ourselves. Everyone in the club deserves that reward.”

Mauricio Pochettino presumably agrees with the defender but the manager made clear before Tottenham’s third-round victory over Tranmere that his focus is on other competitions. “If you don’t finish how we have finished [in the league] in the last three seasons but win the FA Cup, I don’t know if Daniel [Levy, the Spurs chairman] would have too much patience,” he said. “My ambition is to win the Champions League or the Premier League. That’s what puts you in a different level.”

Tottenham beat Palace 1-0 when the sides met at Selhurst Park in the Premier League two months ago but on that occasion Pochettino was able to call upon Harry Kane, Dele Alli and Son Heung-min, three players who are unavailable to him this time around. The Argentinian is likely to field a similar side to the one that started at Stamford Bridge on Thursday. That would mean a place for Eric Dier who, along with the substitute Lucas Moura, missed a penalty in the shootout.

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“Eric and Lucas are maybe a bit more disappointed than the rest but they showed so much responsibility,” said Vertonghen. “Eric was the hero at the World Cup and [against Chelsea] he missed. Fair enough. Lucas the same thing.”

Meanwhile Roy Hodgson has dismissed those criticising Pochettino for a lack of trophies as “naive” and praised his opposite number’s impact over the past five years at Spurs. The Palace manager dealt extensively with Pochettino when his England side trained at Tottenham’s facilities, and the pair are still close.

“People should wise up to what football is today and stop talking about trophies,” said Hodgson. “They should look at the fact he’s taken over a Tottenham team who, really and truly, are having their longest spell as being considered title contenders, Champions League contenders, while bringing through loads and loads of homegrown players. What’s a trophy got to do with it?

“Mauricio’s good. Anyone who watches Tottenham would have to be an admirer of the way they play and the way they go about their business. The manager is an integral part in that.

“If you’re only going to call managers who have won a trophy any good, then basically you have four or five. When was the last time a Bayern Munich manager didn’t win a trophy? When was the last time a Barcelona manager didn’t win a trophy? How do you win a trophy ahead of Barcelona or Bayern Munich? Or Malmö in ‘85 [with whom he won the Swedish league]?

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“If the be-all and end-all of your ability is whether you’ve got a trophy to your name, I find that hard to understand. It’s so naive in terms of what the job of being a football coach is all about. You are just dooming 97 to 98% of all the people working in football as failures because they may not have a chance of winning a trophy. What about the Rotherham manager? He might be doing a great job. Is he going to be a hopeless manager all his life because he never wins a trophy? I don’t see it.”