The Gers produced a stirring performance in the second 45 minutes to overcome the La Liga side, marking another famous evening in the competition at Ibrox.
Speaking to RangersTV after the victory, Davies commented: "I thought it was a tough game, but a good game overall.
"We were disappointed in the opening half hour that we couldn't get our foot on the ball and make passes, but I thought towards the end of the first half when we did that we looked the better side.
"The manager said at half-time that we needed a big second half and to believe in ourselves more, make the passes, and I thought we put in a big second half performance.
"If you keep clean sheets then you can't lose games, which is a good start. It's something to build on."
The decisive goal arrived midway through the second half for Michael Beale's side, with Davies and Abdallah Sima both reacting swiftly to the loose ball from three yards out.
The defender was also gushing in his praise of the Ibrox crowd, who roared the side forward in the second 45 minutes.
He continued: "They were a massive help. You always have a chance at Ibrox with the crowd, and certainly towards the end of the game they pushed us through.
"I thought I kicked it in, but Abdallah is saying that he kicked it in, so I'm guessing both of us kicked it at the same time.
"He was in the net and couldn't get out, and I just ran off celebrating, so it looked like it was my goal. I'm not entirely sure, but I'm happy to give it to Abdallah."