The 22-year-old believes that the team showed its "true class" in the match at White Hart Lane, while also insisting that Spurs are ready for the Premier League run-in.
Rafael van der Vaart put the hosts ahead in the first half with a splendid finish, but the Dutchman's effort was canceled out by another good goal from Gylfi Sigurdsson. Two late headed goals from Emmanuel Adebayor secured a crucial three points for Harry Redknapp's men.
The victory means Spurs now trail their north London rivals by just one goal and the Welshman is now looking for the team to climb back above Arsene Wenger's men.
"We knew the results yesterday, we knew what a massive win it was for QPR to beat Arsenal. It gave us an opportunity to get back level with Arsenal and hopefully go above them," he told Sky Sports.
Before the clash at White Hart Lane, Spurs had only won one out their last six Premier League ties. The 22-year-old believes the run was down to luck but did admit the win was crucial.
"We've been playing well," he told the European sports outlet. "We've had quite a lot of bad luck but we showed what we can do on the pitch here today against a great footballing side like Swansea, and got the vital three points to put the pressure on the others."
The former Southampton man applauded Swansea's brand of football but suggested that Spurs hit top form on the day and took their chances well.
"The way they play the ball is just unbelievable and it's full credit to them. They've been fantastic this season but we showed our true class today," Bale continued. "We showed what attacking prowess we [have] and we punished them when we could."
The London outfit had been flying earlier in the season but its recent dip in form led many to write off its Champions League qualification chances.
However the winger believes that the side is back to its best, insisting that it is confident of ending the season positively.
"We were just saying, me and Younes [Kaboul] 'We're back now'. We feel like we're playing well," Bale added. "I think at Stoke was the tuning point, when we got the last minute equalizer. The confidence is building and [we're] ready for our run-in."