"I've said all along it will take time," Davies told Setanta Sports 1. "In the last few years we've not started particularly well and it's been the same this season.
"We had good pace, moved the ball around very well, created a lot of chances and thoroughly got what we deserved tonight."
"I felt all week the pulse was coming back and the players were looking more like themselves. I felt it was a matter of time until we produced a performance like we did tonight.
"Now we're up and running and there is an awful lot of hard work ahead of us."
Newcastle boss Sam Allardyce described Miller's winner as "a sickener" and lamented the effects of the international break.
He told Setanta Sports 1: "We're disappointed because the sad thing for me is when you have 14 away on international duty for the best part of 10, 12 days, and can't get hold of them to come back and get the team in order - it was apparent tonight.
"We're new together anyway, we didn't really want the international break after the result against Wigan.
"Saying that, it came down to poor finishing for us tonight.
"In the end we were beaten by a wonder goal. Sometimes you have to hold your hands up, there was very little anybody could have done with what the strike was about. Probably 49 times out of 50 it would go over the bar.
"Tonight it went into the back of net. It was great for Derby, and a bit of a sickener for us."