Replays showed it was the correct decision to disallow the goal and Kane, who scored six times in his previous four games against Bournemouth, then limped along the touchline before disappearing down the tunnel to be replaced by Erik Lamela.
He later left the stadium on crutches and with his foot in a protective boot.
Pochettino says that it is now a case of waiting for the England global to undergo a scan on Monday before finding out the extent of his latest layoff.
Manager Mauricio Pochettino confirmed to Sky Sports reporter Greg Whelan at half-time that the injury was "in his right ankle, possibly ligaments, similar to the injury sustained against Sunderland early last season".
"It was between him and the doctor".
"He felt that when he ran and twisted his ankle that it was impossible to stay on the pitch".
Pochettino added: "Every player is frustrated to get injured but he is relaxed now and always thinking positive". He's happy with the victory for the team, disappointed of course with his problem.
"But if you're positive you start the recovery from injury from now".
While Tottenham's win keeps it in a strong position for now, it will desperately hope that Kane is fit to return for its next league game, against Chelsea in three weeks' time. We concede the first goal, but I think the team was better than Bournemouth, and the attitude was great. The Premier League's joint top scorer - tied with Liverpool's Mohamed Salah on 24 goals this season - is expected to lead the attack for England at this summer's World Cup in Russian Federation. They may be out of the Champions League but they are chasing a top-four Premier League finish and have an FA Cup quarter-final clash against Swansea next weekend.