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The Spurs striker went off 14 minutes from the end of Sunday’s success at Wembley after receiving treatment in the first half.
Pochettino also believes Dele Alli will recover from a hamstring problem in time for his club’s next game with north London rivals Arsenal, even if he is missing England duty for the matches with Germany and Brazil.
But he was unsure whether Harry Winks will have to withdraw from Gareth Southgate’s squad after the midfielder went off with an ankle injury in a below-par victory where Spurs failed to hit the heights of their thrilling midweek 3-1 success over Real Madrid in the Champions League.
“Kane was subbed because after 75 minutes we wanted to protect him,” said Pochettino.
“After Real Madrid it was such an emotional game, it was better to avoid risk. I think he’s OK and I’m sure he will go with the international team.”
The former Southampton manager added: “Harry Winks twisted his ankle in the first half, it’s a little bit painful, we must assess him with our medical staff and the national team medical staff.
“He is so excited to be with the national side but now it is up to the medical staff to assess the player.
“Dele felt his tendon at the end of the Manchester United game close to his hamstring and then played 90 minutes v Real Madrid. It is a very small thing. It was not a massive risk to play him here and we hope he can be ready for Arsenal.”
Spurs were disappointing against Palace in a match where the deadlock was not broken until the 64th minute thanks to Son Heung-Min’s 20-yard drive.
“It was very difficult,” admitted Pochettino. “We knew after Real Madrid it would be a massive challenge to compete again. In the end I’m very pleased, the team was very professional.
“It was a game where we had possession and dominated but we conceded a lot of chances. You need some luck to win and it was a good performance.”
– ‘Deserved more’ –
Palace remain bottom and are five points from safety but the Eagles can feel aggrieved with Wilfried Zaha missing their best chance when he fired wide at 0-0 after rounding debutant goalkeeper Paulo Gazzaniga.
“I will be leaving Wembley as a loser, which didn’t happen much when I was here for four years,” said Palace’s former England manager Roy Hodgson.
“We created chances and had moments where we were even on top against an illustrious side. We deserved more than what we had.
“But in football you get what you get. You don’t get what some people think you deserve.”
Hodgson added: “We look at the table and we are still on four points. But globally there is not a lot I can accuse my players of. The confidence is fragile but when the goal went in we could have collapsed and lose by three or four.
“They (Tottenham) have players who can punish you. That’s a positive they didn’t.”
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