A Matthew Pennington strike in the first half proved decisive, as the Birkenhead-based outfit took all three points.
Davis told reporters: "It was a difficult day. We got into a scrap which is how they wanted it to be.
"We tried to get the ball down and play and quicker, but I don't remember a real effort at goal in the first half.
"Second half we were much better but did not have the quality to may it pay in the final third."
The Railwaymen currently sit a point and a place above the League One relegation zone.