Kane notched his eighth treble of 2017 - and his second in the space of three days - to help Spurs to a 5-2 victory over the Saints at Wembley on Boxing Day, breaking Alan Shearer's long-standing record of 36 Premier League goals in a calendar year.
The hat-trick also saw the England international end 2017 on 56 goals for club and country - more than any other player in Europe's top five leagues - to end Lionel Messi and Cristiano Ronaldo's dominance of that statistic.
"Harry is world-class,. Of course, Messi and Cristiano are different. Today – one striker in the world, a specific position – who is better than Harry? It's difficult to say he's the best but he's shown to everyone he's one of the best," Pochettino told reporters.
"Both of his records are massive – to break the Premier League record set by Alan Shearer and then, if you see that over the last seven, eight or nine years, it's always Messi and Cristiano and now, it's Harry as well.
"Becoming better may be a very small step of improvement but when you are at this level, you need to fight with all your determination to keep at this level. To do this, you need to work hard, more than before, be more professional and more focused. If you achieve something and you say, 'If I need to run 10 metres but I will run only nine,' you will cheat yourself, and that is a massive problem.
"The most important thing is to keep the same mentality. The secret is to work hard every day. You cannot say no for one day. That is the secret of the big players like Harry, Cristiano and Messi. You cannot afford not to work every day."
Kane is now also just one goal behind record holder Teddy Sheringham in Tottenham's all-time Premier League top-scorers list.