Kane, who jointly leads the league scoring charts with Liverpool's Mohamed Salah, injured ankle ligaments during last Sunday's 4-1 victory over Bournemouth but Pochettino is confident the forward will return before the end of the season.
"We are talking about one of the best strikers in the world," the Argentine told reporters on Thursday.
"Of course we are going to miss Harry because it's obvious he is one of the best, but we are calm and relaxed because we have enough quality to play and win games.
"It is no excuse now that Harry is out for a few weeks that we are not going to have the same mentality and try and win the games."
Tottenham were knocked out of the Champions League by Juventus last week, and Pochettino said their exit from Europe's elite club competition had left Spurs with two remaining targets - a top-four finish and winning the FA Cup.
"Juventus was a massive game and this is a massive game as well if we want to have the option of winning a title at the end. This is the only option we have to try and achieve that," he added.
"The FA Cup along with the Premier League is now our priority."
Spurs are currently third in the league with 61 points, 20 behind runaway leaders Manchester City.
(Reporting by Simon Jennings in Bengaluru; Editing by Toby Davis)
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