Of all the men that Pochettino could lose, none will be more sorely missed that Harry hot Spur.
Pochettino said he is concerned by Kane's injury - a similar one kept him out for almost two months last season - but praised his side's character in fighting back.
"We need to, in the next week, manage him".
Ten minutes into the second half, Tottenham nearly took the lead when Christian Eriksen unleashed a powerful long-range shot which looked destined for the bottom corner, but Asmir Begovic produced a fantastic fingertip save to deny him.
While the Spurs had a double whammy of injuries, it didn't seem to affect the rest of the team as they beat Bournemouth 4-1, with Heung-min Son netting a brace, while Dele Alli and Serge Aurier also got on the score-sheet.
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David Luiz, Ethan Ampadu and Ross Barkley are all expected to miss out, but the latter may be back sooner than his counterparts. The gaffer hints that he trusts the two forwards but refused to guarantee them a place in the starting line-up against Palace.
Kane suffered two ankle injuries last season and missed 14 matches as a result - the last nearly 12 months ago to the day. He is a great player and if it is a serious injury we will miss him.
Tottenham were down 1-0 at the time of Kane's withdrawal, though Dele Alli quickly equalised to make it 1-1 at the Vitality Stadium.
Kane's global team-mate Dele Alli also seemed to pick up an injury on the south coast, suffering a problem with his groin.
"After Wednesday, it was a massive challenge, the opponent is waiting for you, but the team showed great personality and character, and we fully deserved the victory". "We took only 18 games to get nine clean sheets at the start of the season and since then we've had to wait 11 games which is sometimes frustrating".
"Only fatigue, they're okay, I think in the week they're going to recover", stated Pochettino to Radio 5 Live.
"The three points for us are massive and I am so happy because the three points have put us in a very good position in the table and in the battle for the top-four".