Spurs secured all three points with a 1-0 victory after peppering the Palace goal for much of the second half.
It was Christian Eriksen who broke the deadlock with a stunning strike from range and Kane, who teed up the Dane for the 78th-minute winner, praised the nature of the victory at Selhurst Park.
He said on Sky Sports: "We knew our time would come and what a strike by Christian Eriksen! It is unbelievable.
"This is a tough place to come and we had to keep fighting. We knew we had to bounce back after the weekend and what a performance by everyone.
"We knew we had to dig deep and get a goal. It was a perfect win in the end."
Of the Eriksen goal, Spurs boss Pochettino added: "I'm very pleased for him [Eriksen], it was an unbelievable goal.
"From my position, it was a golazo!"
The result saw Tottenham bridge the gap with league leaders Chelsea to four points with five fixtures remaining.