The Spurs midfielder, who was on Thursday night given the Football Writers' Association footballer of the year award to add to the PFA player and young player of the year trophies he has already won, said the club was "doing everything right" and that he and they had "grown together" over the years.
Bale is expected to be offered a four-year contract in the summer in recognition of a stellar season, amid increased confidence among the Spurs hierarchy that he will be persuaded to stay.
"We set our agenda at the start of the season to qualify for the Champions League. We want to finish in the top four and it will feel like a disappointment if we don't get there," the 23-year-old told the Guardian.
"The club has grown every year and I've become a better player every year. We've had a taste of Champions League football and that's where we want to be again. That's where the club needs to be to get to the next level. That's what we're trying to do this season to lift the club to better things."
The 2-2 draw at Chelsea left Tottenham's fate out of their hands in the race for the top four but the manager, André Villas-Boas, has told supporters to "keep the faith" for their final two matches against Stoke and Sunderland.
Bale, who has taken to a new central role this season to devastating effect, lauded the progress made under the chairman, Daniel Levy, since he joined six years ago from Southampton and said he and the club shared the same objectives.
"I want to play at the highest level possible and be playing against the best teams in the world. I think the club is going in the right direction. All our objectives are the same, we just have to try to achieve them now," he said.
Bale, unveiled by BT as one of a number of ambassadors for its new sport channel, has thrived on the extra responsibility handed to him by Villas-Boas and said the squad was the best he had played in.
"We're all working well as a team. We're all working together. The club is going in the right direction, bringing in better players every season," Bale said.
"The likes of Mousa [Dembélé] and Jan [Vertonghen] have been fantastic additions to the squad and I'm sure we'll bring in a few more players into the squad again this summer. It's just a matter of progressing for everyone and reaching our targets."
Bale, who has scored a string of spectacular and crucial goals this season, said he was comfortable with the elevated level of trust placed in him by Villas-Boas.
"When you're younger, you're quite daunted by the manager. As I've got older, I've also got a lot closer and become a more important player so you speak to the manager more," he said.
"This year I've been handed a lot more responsibility, which has been great. I believe I've been able to motivate myself and make myself a better player by it."
He also paid tribute to the careful husbandry of Tottenham's resources under Levy and said it was important that the club had been able to grow in a sustainable way, particularly given the introduction of the Premier League's financial rules.
"Everything has changed. When I first arrived there was talk of a new training ground and a new stadium. As the years have gone in, it's got better and better. The training ground has happened and next it'll be the stadium. The club is growing and I think it's growing within its own means," he said.
Drawing a distinction between Spurs and other clubs that had spent beyond their means, he said: "That's why the rules are in place now. We've seen a lot of clubs before that have made that mistake. But Tottenham have shown they can make a profit every season and they're doing it the right way. Everyone is in the same boat and they're doing everything right."
Senior Spurs insiders are increasingly confident Bale will stay, even if they miss out on the fourth Champions League place, and the player believes that the squad have matured together and are hitting their peak.
"We're all of a similar age. We're all around our mid-20s. We've been playing together for three, four, five years," he said. "We've got a good firm English base there as well, which is always important for a club like Tottenham. We're heading in the right direction and hopefully there is still a lot more to come from the team."
Bale also insisted there is "a lot more to come" from himself, that he is on an "upward slope" and still learning what was required of him in a more central position.
Asked how he could improve on his impressive season, he said: "Score more goals. More with my right, more with my left. I think you just have to keep going, keep plugging away. Even your best players – if you look at Lionel Messi, [each year] he scores more goals than he has any other year. Cristiano Ronaldo is the same. There is still plenty more to improve. I just have to keep my focus at this level and take it further."
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image: © James Boyes