A double from James Tavernier and an Abdallah Sima strike sealed the win for Gers, with the interim boss delighted to pick up the points in Paisley.
Speaking to RangersTV at full-time, he said: “We knew it was going to be a really difficult place to come with the start they have made to the season and how well organised they are.
“We just have to take all the positives we can from today, three goals, a clean sheet and three points so it is a step in the right direction, certainly.
“The first goal is always important in these types of games and then they go down to 10 men. At times I felt we could've moved the ball about better and we made it more difficult than what we had to for ourselves at that point.
“It is a small step in the right direction and I'm sure it'll give everyone a little bit of a lift, but we know that there's a lot of work still to be done.
“It was always going to be a tough ask coming off the back of the game on Thursday night, it was a really quick turnaround in terms of the time and the travel. I felt like the boys' application and desire to try and do everything right was really positive and I just thanked them for that.
“I am delighted for everybody in the dressing room and the fans as well because they needed something to cheer about a little bit. We know there's still a long way to go but there are certainly positives today.”
On goalscorers Abdallah Sima and James Tavernier, Davis continued: “Abdallah has been a real threat, he offers that attacking outlet that you want and gets into the areas in the box.
"He has been able to finish them on a regular basis so he has been in a good place and hopefully after today a few more will be heading in that direction.
“The third goal was an unbelievable strike, Tav has got that in his locker as we know, and I was surprised a few times earlier on in the match when he got into those sorts of positions that he wasn't having a go.
"It was an incredible strike and again the numbers that he produces year after year in an attacking sense are quite incredible for a full-back.”
Davis says belief is key for the squad, as they look to continue to build when they return from international break. He continued: “As I said to them in there, we have to be positive and I do believe there is quality in that dressing room.
“Of course, whenever you are in those moments confidence is dented and belief is dented a little bit but we just have to believe in ourselves and keep working hard. The performances will hopefully continue to improve and will gradually build again but it is nice to finish on a win this week.”