Kane rolled his ankle in a collision with Bournemouth's Asmir Begovic while scoring a goal, which was then disallowed by referee Mike Dean.
"Yes we are concerned because we still don't know what's going to happen with him", Pochettino told the BBC.
"Of course I worry about him, his ankle, we hope it's not a massive issue for him and the team, and as soon as possible can recover again and be available".
Bournemouth started positively and nearly took the lead in the fourth minute when Junior Stanislas broke through on goal and rounded the keeper, but he saw his effort come back off the post. "We are concerned but need to wait".
Kane suffered two ankle injuries last season and missed 14 matches as a result - the last nearly 12 months ago to the day.
Megan Markle's secret baptism with water from Jordan River
The baptism is a mark of respect to Queen Elizabeth II, who is the head of the Church of England. According to CNN , Markle personally asked Welby to perform the ceremony.
South Korea forward Son now has seven goals in his last four games in all competitions and his fine form has been a major factor in Spurs' 12-game Premier League unbeaten run.
Tottenham came from behind to move up to leapfrog Liverpool into third thanks to a double from Heung-Min Son and goals from Alli and Serge Aurier.
Pochettino added: "I think he's having a fantastic season - the best season he's had since he arrived".
The result against Bournemouth means that Spurs are now third in the Premier League table with 61 points from 30 matches, just four points behind second-placed Manchester United. He's netted 24 goals this season, but so has Mo Salah.
Home boss Eddie Howe replaced Mousset and Daniels with Josh King and Jordon Ibe as he looked for a way back into the game, and Francis tried his luck with another long-range strike only to see it fly over. "The most important thing is to win and so it was defeats that were more frustrating".