Tottenham, who were fourth last season, have gone close to conquering the Premier League under Mauricio Pochettino – a runners-up finish in 2016-17 sandwiched between third in 2016 and 2018.
Spurs, however, have bolstered their squad after two consecutive windows without a signing – club-record recruit Tanguy Ndombele, who scored against Villa, Giovani Lo Celso and Ryan Sessegnon headlining the arrivals.
And Spurs star Kane is confident Tottenham can push champions Manchester City and Liverpool all the way this term after his brace in the win over Villa.
"We kept with them for a while last year but they blew ahead after January," Kane said. "We have to make sure we get off to a good start. Liverpool set the standard on Friday night and City on Saturday afternoon, so it's important that we stay in touch as long as we can.
"We have full belief that we can go all the way but there's a long road ahead. That's why we buy players: to strengthen the squad and have more competition for places. That's what we've got.
"We've got a good, hungry squad. Everyone's fit and ready to go. The players that came on have to try to make an impact and they did. It's important for us if we're going to have a good season. Of course, it's just the start now but throughout the winter time when loads of games are popping up we need everyone to contribute as much as possible.
"I think it's definitely going to help us when we start getting into the thick of it, with games midweek. I haven't really had a chance to see Ryan and Gio train yet but I obviously look forward to that next week, settling them in and I'm sure they'll want to come and make a big impact as well. Everyone here is trying to move in the right direction and that's what we're trying to do."
Tottenham trailed Villa 1-0 at half-time but Christian Eriksen – who has been linked with a move away – came off the bench to inspire Spurs.
Eriksen reportedly opted against a move to Manchester United as the Denmark international holds out for a switch to LaLiga, where Real Madrid and Atletico Madrid are believed to be interested.
Despite uncertainty over Eriksen's future, Kane added: "Obviously I've been playing with Chris now for five or six years and we all know the qualities he has: the assists, the passes, the goals. Whether he starts or is on the bench, the most important thing from all of our points of view is that he gives everything for the team.
"Obviously, there's been speculation about his future but as long as he's training hard and playing as hard as he can when he's here, that's all we can ask for. What will be will be but we're happy to have him.
"That's all the fans ask for as well: commitment. We're happy to have them. We'll see what happens but from our point of view we've got a strong squad and we'll use that throughout the season."