We could have scored more - Two-goal Kane hails 'unbelievable' Tottenham
The England international scored twice at Wembley and also teed up the second goal for Son Heung-min, while Dele Alli joined his team-mates on the scoresheet.
But Kane, who had not previously netted at the national stadium in the Premier League, believes Spurs could have further humiliated Liverpool and their generous back line in a rampant display on Sunday.
"[It was] unbelievable. We wanted to start fast and get the crowd on their feet and that's exactly what we did," he told Sky Sports.
"When it went to 2-1, we had to stay focused. We knew we'd get more chances and that we had to take them and then we did really well in the second half to see it out.
"We could have scored more. We could have got the third and fourth early on. Their goal came against the run of play but that's football. We gave them a sniff and they took it but, after that, we played really well.
"Defensively, we were really solid. They didn't create much and we were very good on the counter."
29 - Harry Kane has scored his first @premierleague goal at Wembley for @SpursOfficial with his 29th shot at the stadium. Duck. #TOTLIV pic.twitter.com/ctebtwS5Ym
— OptaJoe (@OptaJoe) October 22, 2017
Tottenham have a number of key fixtures coming up, playing Manchester United, Real Madrid, Arsenal and Borussia Dortmund, among others, in the coming month.
And Kane is hoping this victory can spur his side on in those tests.
"We're in very good form. We've got a tough month, [but] we've started it well," he continued. "We're positive, feel good and this will give us more confidence going forward."
Son added: "We deserved to win - the early goal was very important from this monster [Kane].
"We have to just keep thinking positive like we did. We work really hard every home game to get three points. We have to just keep up the performances like [this one], work hard together and show it on the pitch."