Kane damaged left ankle ligaments near the end of the 1-0 loss to Manchester United at Wembley on Sunday after being sandwiched between Victor Lindelof and Phil Jones.
Tottenham are already without their South Korea forward Son Heung-min who left after the United game to join up with his country at the Asian Cup which runs until the Feb. 1 final.
But France midfielder Moussa Sissoko, who pulled up with a groin injury just before halftime in the United defeat, should be fit for the League Cup semi-final second leg at Chelsea next Thursday. Spurs lead 1-0 from the first game at Wembley.
Pochettino said it was "tough" to be without "one of the best strikers in the world" for the next six weeks, but added that it could be an opportunity for the academy players.
"It didn't change (the club's approach to the January window) all that happened with Harry," said the Argentine.
"Son we knew was involved in the Asian Cup for a few weeks. We were always open to improve with Harry in condition or not, but at the same time we know it is going to be tough and difficult to add the player that we want.
"It didn't change our mind, I think it's a very good opportunity for players to play more, to step up. I'm sure it's going to be a good opportunity for young players through the academy to show their quality."
Pochettino has brought several youngsters through to the first team squad with midfielder Oliver Skipp and Argentine defender Juan Foyth having played this season.
But he is likely to rely on experienced Spanish forward Fernando Llorente as a replacement for Kane, while speedy Brazilian forward Lucas Moura should soon be back from injury.
"We know what it means to have Harry Kane fit and available to play and help the team to win, but we have a squad and (his absence) can't be an excuse.
"In the next game we need to play against Fulham (in the Premier League on Sunday) and the semi-final second leg with Chelsea with the same mentality - thinking we can beat any team."
Third-placed Spurs are nine points behind leaders Liverpool and five off Manchester City but Pochettino said it was not impossible to fight for the title with 16 games left to play.
However, he added: "For me the realistic contenders (to win the Premier league) are Liverpool and Manchester City."
(Writing by Ken Ferris; Editing by Toby Davis)
