The midfielder was outstanding again for Gers, and it was his shot which rebounded into the path of Alfredo Morelos to win the game late-on for the Light Blues.
Speaking to RangersTV, Davis said: "I think you know what you are going to get every time you come here.
"You are going to have to compete first and foremost and try to win the battles, and I thought we stood up to that challenge really well and it was just a matter of being patient and keeping on trying to do the right things.
"Luckily, Alfredo got the winner for us in the end."
Staying patient to eventually get goals has been a major trait of this Rangers side this season, and Davis continued: "That has been a huge positive for us this year. I think that comes with the confidence of getting results by doing it that way.
"We have certainly learned from the past and believe in our quality and we have to just continue to show that and even in games where there are spells where it is difficult, we just keep believing, keep doing the right things and more times than not we have found the answers this season."
Alfredo Morelos’ strike came off the back of a magnificent performance from him against Antwerp in the Europa League last Thursday night.
Davis said of him: "He caused their centre-halves a lot of problems tonight and everyone knows it was a penalty in the first half so for that to go against him, and for him to keep his nerve and keep doing the right things, I am delighted for him to get the winner at the end."
The clean sheet also thrilled Davis, who added: "That has been a big bonus for us.
"We know they are going to play direct at times and are going to ask questions of you and try to turn you, and I thought we stood up to that challenge really well, so I am delighted with the defensive display and another clean sheet and three points.
"We move onto the next game now."
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