The European champions - who achieved 'La Decima' last season - underlined their threat in the competition with a convincing Group B triumph on Tuesday.
And Bale, who scored Real's second goal with a measured two-touch finish in the first half, was content with the performance, which helped to ease some of the frustration of Saturday's 2-1 La Liga loss to rivals Atletico Madrid.
"We knew that we needed to start the game well after some poor results, but we showed what we're made of," the 25-year-old told ITV.
"We felt we needed to get back on track and that's a good way to do it."
A poor start to the league campaign, which has yielded just three points from three games, has left coach Carlo Ancelotti under some pressure, but Bale insists that is not a factor in his own approach to matches.
"I just concentrate on the football, I don't listen to anything like that," he said.
"I think we go out on the pitch, try to enjoy ourselves, play our best football and hopefully we win - thankfully we did that."
Real return to domestic action with a trip to Deportivo La Coruna on Saturday as they eye just their second win of the league season.
