Kane netted twice in Spurs’ 4-0 win over Everton at Wembley, moving him to 98 Premier League goals and one clear of Teddy Sheringham.
Both of Kane’s strikes came in the second half, with the first coming when he got a toe on Son Heung-min’s cross-cum-shot in the 47th minute.
“When he shot I thought it might be going in but luckily for me it wasn’t,” Kane said on BT Sport. “I might have been offside. Sometimes you get it, sometimes you don’t. Luckily it went my way.”
Kane said he was proud of the record but would not dwell on it for long.
“It’s what I always say, it’s something I’m very proud of but it’s on to the next one, we’ve got to keep going,” he said. “These boys are great, they set me up and we’ve got to keep going and winning games. Hopefully I’ll keep scoring.”
The win keeps Tottenham in fifth, level with Liverpool ahead of their match against leaders Manchester City on Sunday, and three points behind Chelsea after their 0-0 draw with Leicester.
“Whenever other teams around are dropping points you’ve got to be there and to win,” Kane said. “It could have been a tough game but from the start we were really on it and deserved the win.”
Manager Mauricio Pochettino called it a “massive three points” as Tottenham bid to break into the top four.
“It was a fantastic performance, I’m very pleased, I think we fully deserved this in the end, the victory,” Pochettino said. “I’m so happy because for us it was a game that we must win, a massive three points for us today.”
On Kane, he added: “He’s such a talented player, so professional and I’m very happy. Congratulations to him, he deserves all the credit and the praise. This way he’s going to break all the records in the Premier League and in England, and it’s fantastic because he helps the team every week.”
Everton had the ball in the net first but Wayne Rooney was correctly ruled offside. While manager Sam Allardyce was left to rue the fact the same verdict was not given against Kane as he put Tottenham 2-0 up, he pulled no punches in his assessment of what came next.
“But for Jordan Pickford they would have had more today and I’m hugely disappointed in the professionalism of my players today,” he said.
“It’s hugely out of order that you relinquish that defensive responsibility when you’ve just gone 2-0 down. There’s still another 44 minutes to play. You play your way back in and be professional about it.
“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. We’ve got to cut it out and we’ve got to cut it out starting tomorrow.
“Tottenham can beat anybody by a lot of goals but they should have had to work harder than they did.”