Davies believes his team have started to show the form he knew they were capable of during recent struggles.
He said: "After all the painful times we've had over the last 18 months, we're making progress.
"We're trying to build a style of playing here whoever is available and it's coming along.
"And to play with the desire we did in the second half, even if it was bit scruffy, kept us in the group."
The former Wales forward had special praise for young skipper Sam Hobbs.
"The way he led the side was magnificent," he said.
"A lot of our youngsters did tremendously."
Now the Blues have to repeat the job next Friday at Scotstoun.
"Glasgow are a top side and they'll be champing at the bit," said Davies.
"We've got to be ready for that. We're going to have to do what we did tonight and then some more."
His Warriors opposite number, Gregor Townsend, was generous to the Welsh region.
"Cardiff showed what a good team they are and they also showed how much they wanted it," said the former fly-half.
"We've got to do that next week - and more.
"I thought we played pretty well for the first 15 minutes, but couldn't get points on the board. Then they got their tails up, but we still had the belief to play better in the second half.
"In the first half we didn't work hard enough in attack. You have to go through the phases and we were trying to go too soon. We couldn't get much momentum in the set-pieces and that makes it difficult to get your game going.
"We simply need to produce a better performance next week."
An incredible 75-yard gallop by Lions wing Alex Cuthbert clinched Cardiff's victory.
Rhys Patchell had crossed in the first half and kicked a penalty, while another Wales international, Leigh Halfpenny, contributed 16 points with the boot.
Glasgow's points came from tries by Sean Maitland and Leone Nakarawa, with both being converted by Duncan Weir who also kicked two penalties.