The O’s beat Billericay Town 2-1 at the New Lodge – a game he said was encouraging against a team expected to earn promotion next season in the Bostik League after a summer of impressive signings.
Davis will talk to director of football Martin Ling next week to discuss transfer plans.
The new boss has targets in mind and after the win he said he wants to try and add a new face before next weekend.
“I think we’re possibly one player short,” said Davis after the win in Essex. "We're looking at it.
“If we can bring that player in prior to the game with Sutton United on Saturday then we’ll be delighted.
“Some of our football today was really pleasing on the eye, so I’ve got to be happy.
“It was important a lot of our lads got 90 minutes today, the season is fast approaching and we’re feeling good.”