Kane endured a slow start to the new campaign, scoring just once in his first 13 matches, but he netted a hat-trick in a 5-1 win against Bournemouth earlier today.
And Pochettino was delighted for the 22-year-old striker, stating that he should have become a stronger player for overcoming his goal drought.
"I'm very pleased for Harry," he said, quoted by the London Evening Standard. "I never had any doubts about him, but it was very important hat-trick for him," said the Argentine coach.
"It's important for him to learn from that period. It happens in football. I'm happy because he'll become a much better player after such a tough period.
"He will score a lot of goals, but football is not about just scoring. He works very hard for the team."
Pochettino's faith in Kane's ability was highlighted over the summer transfer window, when the Argentine boss didn't bring in another centre-forward.
Kane is currently the only out-an-out striker in Spurs' squad, and he is required to carry much of the side's goalscoring responsibility.
The pressure did appear to be weighing him down over the early part of the season, but after netting a hat-trick against Bournemouth he should be much more confident.
Kane now has four goals for the campaign, and he will be hoping to add to that tally next weekend, when Spurs take on Aston Villa, looking to take their unbeaten run in the Premier League into double figures.