On-loan Finn Lauri Dalle Valle netted his third and fourth goals of his short stay at Gresty Road as the Alex cruised to victory with a second-half performance as dominant as their first-half showing was inadequate.
The Railwaymen men have now lost only one of their last seven games and Davis hopes results like this and the midweek draw at Sheffield United will help convince his players they belong at the business end of the table.
Davis said: "This win was very important. This week's results have given us the belief that actually we're not a bad team and we should be in that top seven or eight in the league. It is a young team and we won't get carried away. I targeted 30 points by Christmas and we are nearly there so I'm delighted with our progress so far.
"They knew when they came in at half-time that I was going to say some unpleasant things and they were ready for it. They knew they could do better.
"I don't know what it is about our first-half performances. They always respond to my half-time talks so maybe I need to do my half-time talks at the start of the game."