Kane became the first Spurs player since Gary Lineker to reach the 30-mark with a late strike in his side's 3-1 Barclays Premier League victory at Newcastle on Sunday.
However, Pochettino is convinced the 21-year-old England hitman can improve further as he continues to make his way in the game.
He said: "He has big potential. He is young and this is his first full season in the first team. We need to push him to try to improve his level because he has the potential to improve.
"It's a fantastic achievement and I congratulate him. He deserves this moment because he has worked a lot. It's an historic thing.
"He's happy in the changing room and all his team-mates are happy, and I think all our supporters and the club are happy at his achievement."
If it was Kane who put the icing on the cake at St James' Park, it was Nacer Chadli and Christian Eriksen who paved the way for his late contribution as the visitors condemned Newcastle to a sixth successive league defeat.
Chadli fired them in front on the half-hour and after Jack Colback had levelled 20 seconds after the restart, Eriksen scored with a free-kick which evaded all the yellow shirts in the middle and defeated keeper Tim Krul.
Kane killed off any hopes of a second fightback when he rounded off a 91st-minute break to leave Pochettino delighted.
He said: "We fully deserved the victory and the three points. I think our performance was better than Newcastle's and I am very pleased for our players.
"I am happy to recover this feeling after the last two games - that wasn't good and it's important to feel victory again."