The central defender turned in a strong performance next to Connor Goldson in the commanding victory – and he was also fulsome in his praise of a moment of quality from James Tavernier.
He told RangersTV: "I thought it was quite comfortable - I don't think Allan [McGregor] had too much to do - we had a few moments where we can defend better and we need to work on that, but we are constantly working and trying to get better.
"I thought we controlled it quite well and needed the penalty to get the lead for half time.
'We didn't create much in the first-half but we were in control and then the free-kick from Tav in the second half was crucial just after they went down to 10-men.
"I think we looked a bit better in the second half and then it was a moment of quality from Tav that took the game away from them and it was comfortable after that with them having 10 men.
"I'm really happy for Kem[ar Roofe] as well as he has been up and down with injuries, but he gets on the pitch and scores."
Davies continued: "Most weeks the games are similar. It was my first time playing here and I'd heard about the pitch, but I thought the pitch was good as it had rained, so there were no excuses there.
"I think we can play better but we are picking up wins which is the main thing."