'Amazing' Kane continues to surprise me – Pochettino
Kane opened the scoring after just seven minutes at Turf Moor, converting a penalty in emphatic style after Dele Alli had been fouled.
He then made sure of the victory in the second half with goals in the 69th and 79th minute, taking his tally for the year to 36 in the Premier League, equalling Alan Shearer's record.
And Pochettino was elated for the striker, waxing lyrical about his star man, who he thinks could have scored even more.
"First of all I have to congratulate Harry," Pochettino told BT Sport. "It's the same record as Alan Shearer.
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"He is amazing, a fantastic player, he needs one more to be above Alan – we will see the next game.
"But it is fantastic for him, he could have scored more than three today because the chances were there.
"I was a little bit frustrated we have not scored more – there was a massive chance for Son [Heung-min], for [Moussa] Sissoko, I feel sorry for them, but they need to keep going and the next games they are going to score, no problem.
"It's difficult to find words to describe Harry Kane. Even during my time at Spurs I'm surprised by him.
"The hat-trick is nice for him, but we could have scored more than three. I'm worried when you don't create chances though."
Clarets boss Sean Dyche opted to focus on Alli, who he thinks could have been sent off before winning what he claimed to be a cheap penalty.
"You see them go [get sent off for such tackles]," said Dyche. "He is out of control and you see red cards for that.
"For the penalty he is going down after the contact, which is minor contact at best, so that's a really tough one too."