Messi or fellow La Liga star Cristiano Ronaldo have been Europe's top scorers for the past seven years.
Kane's latest goals came from a header and two left footed shots and as the Guardian put it, he "terrified Southampton every time he picked up possession". He had scored another hat trick just days earlier against Burnley.
Kane said: "I'm very proud. Messi and Ronaldo have dominated football for so long and they're two of the greatest players ever so it's an honour to even be compared to them.
"I'll keep working harder, it's about finding little percents to get better and doing things on the training ground to make you better. There's a great staff here and a great manager here who will keep pushing me, don't you worry about that! I'll have to take [my teammates] out for dinner to thank them!"
Spurs manager Mauricio Pochettino said: "Harry is world-class. Of course, Messi and Cristiano are different. Today โ one striker in the world, a specific position โ 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. Both of his records are massive โ 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."
Among those to congratulate Kane was Shearer, who tweeted: "Well done and keep up the good work."
Kane told Sky Sports it as a"great feeling" to overtake Shearer's mark.
"It was hard not to think about it going into the game being level.
"As always I wanted to win the game first and foremost, but of course I wanted to score as a striker. To get that goal early on and get that record was a great feeling and I could enjoy the rest of the game.
"This year I would say physically I have improved, recovery from games, getting ready, we have such a busy schedule. Just making sure I'm ready for each game, eating right, recovering right with ice baths. I feel really good. I feel sharp and at my best."
He picked out his favorite goals of the year.
"I liked the second one against Huddersfield from outside the box with the left foot. That was nice," he said."That third goal today was good; the third goal against Burnley I think summed up how I play with the tackle and then the touch and finish, so there's been some good goals but hopefully some better ones in 2018."
