Son was named Man of the Match for his display against the Toffees after he was involved in three of Tottenham's four goals scored on the night.
"It was a fantastic performance, I'm very pleased, I think we fully deserved this in the end, the victory", Pochettino said.
The opener came for Tottenham on 26 minutes and, having caught Everton out moving the ball left to right on a number of occasions, that ploy paid off when Serge Aurier found space.
Inexplicably, Son is one of the most under-rated stars in English football and even at Spurs, he is not one of the club's A-listers, lagging behind Kane, Dele Alli, Christian Eriksen and keeper Hugo Lloris.
Kane bagged a brace against Everton to put his side on the front seat after Korean ace Son Heung-Min opened the scoring in the first half.
Victory left Spurs level on points with fourth-placed Liverpool, who face runaway Premier League leaders Manchester City on Sunday, in a competitive race for a place in next season's Champions League.
Everton had the ball in the net first but Wayne Rooney was correctly ruled offside.
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He set a record of 39 Premier League goals in a calendar year in the process and has now joined the former Liverpool captain in the history books.
Everton, meanwhile, is winless in its last four Premier League matches and has lost three games in a row in all competitions.
The 24-year-old also reached the 20-goal mark for the fourth successive season in the Premier League but still lags way behind Spurs legend Jimmy Greaves, who scored 220 goals in 321 First Division appearances.
"Maybe I have a bit of responsibility by playing too much attacking-minded players and not as many defending-minded players".
New Everton signing Cenk Tosun is set for his debut after completing a move from Besiktas and Allardyce has confirmed he's itching to feature.
"It shocked me. I've not seen it since I got here but I've seen it now, and it's probably what was apparent before I got here". I saw some of the good sides of the players last week and I saw some of their worst sides in the second half today, which is massively worrying in terms.
We are blessed to be watching Harry Kane in this form.
And of course, let's not forget he matched his own record on Saturday, scoring in five successive home Premier League games and will be hoping to surpass this against Manchester United in a few weeks' time (January 31).