Neither side were able to find the back of the net and the match ended as a 0-0 draw.
While the first leg finished as a goalless draw, Bale is confident his side will be victorious during the second leg at the Bernabeu.
"Definitely the most important thing from the away leg is that we're still in it," Bale said after the match. "As long as we don't concede it's a good result for us and I'm looking forward to the second leg at home now.
"For me, I thought we should have won, maybe by a few. But I definitely thought we deserved to win. I thought especially in the first half I thought we played probably the best we have against Atletico in the little while.
"Shame we didn't really push on in the second half but, yeah, strong performance that will gave us confidence going into the second leg.
"They're very physical, very difficult. But I think it was a big game tonight, it was very tense from both teams. We'll have to take a nil-nil from the game and go into the second leg full of confidence with the home advantage."
Meanwhile, Real goalkeeper Iker Casillas lauded his opposite number Jan Oblak for being on top of his game during the match.
"He was the hero of the first half," Casillas said. "We deserved more. He was fantastic. Then Atleti didn't allow us to get forward so much and controlled the game better.
"In the second half Atletico had more of the football and were able to calm the game down.
"0-0 leaves the game open for the return and it'll be very nice. It's an attractive game. We hope to have a good game. We're at home and we'll go to win."