Francois Zoko and Yoann Arquin both scored on their league debuts as 10-man County ended Crewe's 20-game unbeaten run before the latter was shown a straight red card for a petutant kick on Crewe defender Ashley Westwood.
Mathias Pogba pulled one back as Crewe sprang into life and the Magpies were hanging on by the end with Lee Hughes clearing Westwood's effort off the goalline.
Davis said: "I haven't had to prepare a losing speech for a while, but it couldn't go on forever. I'm glad it has happened now so we can put it behind us and move on.
"I'm delighted with the way we played and the spirit we showed to come back and work hard and I've seen enough to think we can do well at this level.
"Even though it was a disappointing result, I was encouraged by it in terms of the attitude and the application that the players put in. They were a good side and it was a real test and we gave a decent performance."