Sergio Ramos opened the scoring on the night with two goals early in the first half before Cristiano Ronaldo scored a double of his own, breaking Lionel Messi's record for goals in a single Champions League campaign by taking his tally for the season to 16.
The 5-0 aggregate victory — following a 1-0 win at home a week ago — fires Madrid into the final of the competition for the first time since 2002 and Bale believes the holder's style played into Madrid's hands as it moved a step closer to its 10th European title.
"It's a fantastic result for us," the Welshman told ITV . "I think we've been working hard, we got our tactics right and I thought we played very well tonight and deserved the win.
"I suppose they played into our hands. They always leave space on the counterattacking, which we like. We've got quick players and we have to exploit that. It was a great performance and we're happy to be in the final now. But there's still one step to go.
"You have to do certain jobs for the team in certain games and everyone put in 100 percent tonight. No matter who it was, they put in a performance and it showed in the result. This is definitely why I came to Madrid. This is why I wanted to come to the biggest club in the world. To win trophies, to win massive games. We still haven't won it yet, we've got a difficult game in the final whoever it may be and we're looking forward to it."
Carlo Ancelotti's men will face Chelsea or Atletico Madrid in May's Champions League final.