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Kane was speaking after earning another individual honour, Premier League player of the year at last night's London Football Awards, and in the wake of Tottenham's Carabao Cup Final defeat to Manchester City on Sunday.
The loss at Wembley means Kane is still to win a team trophy as a player but he is on course for more individual awards, as he leads the running to be crowned Premier League player of the year and win a third Golden Boot.
"Individual awards are great, they are fantastic achievements," Kane said.
"When I look back at the end of my career, I will go over it and take in a little bit more. The goal right now as a player is to win team trophies. As much as this [award] is great, I want to be winning the biggest prizes that there is to offer as a team and we are not quite doing that.
“It is one of those [situations], it is bittersweet. I would rather be winning team trophies and this award. It is what it is. I am proud to win it. It means it has been a good season on the pitch, so I have just got to try and continue what I am doing.
“Obviously the Willow Foundation [who the LFAs are in support of] do amazing work. So I am really happy to be taking it home.”
There has been more talk this season of Kane securing the ultimate individual accolade and surpassing Alan Shearer as the Premier League's all-time top scorer.
Kane has moved to within 100 goals of Shearer's record of 260, which would guarantee the current England captain immortality, but he says even that honour would mean less without team trophies.
"When you come to individual achievements, I think that is definitely right up there," he said. "There have been so many great players over the years in the Premier League.
"You look at the names on the top 10, the top 20 and you think of how many goals and seasons they've played.
"For sure, if I finish my career as Premier League top goalscorer and, hopefully, England top goalscorer, that'd be incredible — but it wouldn't feel as good if I didn't have a lot of team trophies to go with that. If I didn't have the Premier League or a European Championships to go with that.
"From an individual point of view, of course that's the end goal, to try and score as many goals as possible and be at the top of those charts. But, for sure, without winning the biggest trophies as a team, it wouldn't feel as good.
“Obviously being under 100 goals away now it feels like it is a little bit closer than maybe in the previous seasons,” Kane added of Shearer’s record.
“But that’s still a lot of goals to score over a few years or so. I am not too focused on it. I just try and take each season as they come.
“We can have the conversation in maybe a couple of years’ time when we are hopefully a little bit closer.”
Kane's hopes of overtaking Shearer would be aided by longevity and the 27-year-old believes he could keep playing well into his 30s.
"I feel like the prime for a good professional footballer should be early 30s, going to mid-30s," he said. "There is no reason, if you keep your body in good shape and do the right things off the pitch, that you can't play at the highest level for a long period of time.
“There are so many examples of the top players playing for many years, and playing at a high level, until their mid 30s to late 30s.
"That's definitely a goal of mine, to be playing as long as possible and it is achievable. I am only 27, so there is still a good amount of years before I even get to that stage. But, for sure, I feel like the aim is to play well into the 30s and for as long as possible."
Spurs can still qualify for the Champions League but Kane admits it has been a disappointing campaign for the club, who topped the League in December but sacked manager Jose Mourinho last week after a sustained downturn in results.
"It has been a disappointing season if I am totally honest," he said. "We have had so many opportunities and been in many games where we have been ahead or in a great position going into the last 15 to 20 minutes, and we have not got over the line.
"When we look back, we were in a great position come November and then that spell over December and January really put a halt to what we were trying to achieve. We have still got loads to improve on. The only thing now is to try and make that Champions League spot.
“Obviously the start of the season, being top of the league come November, it shows that when we are playing well, when we are in a good space, that we are not far away and we can compete at the top of the league.
“All in all, the disappointment kind of overrides that. For me, there are some positives. It is more when we reflect after the season and we look back, I think as individuals as players, everyone likes to see what they can improve on and do better.”