Tottenham have already amassed their record number of points in the Premier League but know that even four more wins – taking their total to 89 – might not be enough to overhaul leaders Chelsea, who are four points in front with four matches remaining.
An 89-point haul would match the work of Manchester United in 2011/12, who lost the title on goal difference to Manchester City and remain the most impressive runners-up in Premier League history.
It will not be easy for Spurs to do better next year than this. They will play home games at Wembley for a single season before moving to their new stadium, a stone’s throw from White Hart Lane, for 2018-19.
Kane said: “We've just got to keep building. We’ve had a better season than last year and again, whatever happens this year, next year we have to get even better. That’s important. We have 77 points, which is seven more than we got last year and there are still four games still to go.
“We just have to try to finish strongly. We've got another game Friday night at West Ham and it's good to play before Chelsea. Hopefully we can reduce the gap to one point and then see what happens.”
Chelsea face Middlesbrough, who are on the brink of relegation, at Stamford Bridge on Monday – one of three home fixtures in their final four.
Kane scored from the penalty spot in the 2-0 win over Arsenal on Sunday, to ensure Spurs will finish above their north London rivals in the league for the first time since 1995.
The England forward added: “Of course it is fantastic to finish above them. The most important thing for us was to put pressure back on Chelsea. Watching them win at Everton meant we knew we had to beat Arsenal and we did it.
“It was an added bonus that in the last north London derby at the Lane, we managed to make sure we’d finish above Arsenal. It's great for the fans and great for the club. But we're thinking about trying to get that title and we'll see what happens.”