Kane seemed to have pulled Spurs level after Junior Stanislas opened the scoring on the south coast, but with his goal ruled out for offside, concerns grew after the England striker remained hunched on the turf clutching his ankle.
"I am concerned, until he has a scan tomorrow we can not say nothing more", Pochettino said.
"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". "You need 24 or 25 players with the same objective - to fight for the team and help the team when the gaffer calls on them".
The win moved Spurs a point and a place above Liverpool into third with 61 points from 30 games and restored a five-point gap over fifth-placed London rivals Chelsea who they visit on April 1st in the battle for the top four Champions League spots. "I don't believe he will be a big problem".
"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".
Spurs climbed up to third in the Premier League table with goals from Alli, Heung-min Son  and Serge Aurier sealing a 4-1 comeback win at Dean Court.
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Dele Alli then restored order ten minutes from the interval, which had come moments after Harry Kane had to leave the field with an ankle injury.
The Bosnian goalkeeper's miserable afternoon was compounded in injury time when he could only swat Kieran Trippier's cross onto the head of Aurier as Tottenham banished memories of their Champions League defeat in style.
"I think he is doing a fantastic season, the best season since he arrived", added Pochettino.
Alli equalized with a composed volley at the back post shortly after Kane went off, but it was Son who won the match.
Bournemouth boss Eddie Howe felt the scoreline flattered Spurs and was unhappy that Callum Wilson had an 84th-minute goal disallowed at 2-1.
"I thought we gave everything to the match, ultimately they were too good for us".