The Chester City boss saw his squad claim a 2-1 victory from their pre-season friendly at non-league neighbours Vauxhall Motors.
Goals from Tony Dinning and Stephen Vaughan edged the Blues to their first pre-season success on the back of a 2-2 midweek draw at Southport.
Davies said: "We could have scored seven or eight goals, so we're creating the chances, but we do need to be putting them away.
"It's not a concern, but it's the same old story with that I'm afraid, but we'll keep working at it and hopefully that will progress.
"But halfway through the second half of the Vauxhall game I was looking forward to the Carlisle and Swansea City games, because they are two teams that should be better than us on paper.
"We've had two games now that, with all due respect, we've gone about our business, and passed the ball, but it's just a touch false for us."
Davies, who included trialist Trevor Benjamin in City's starting line-up at Vauxhall, added: "I think you always know what you're going to get from the big man. He isn't a player that is going to run into channels, but if you can put the ball with a bit of quality in or around him he will hold the ball up.
"He got us the penalty and he's played the same throughout his career and he showed that for us on Saturday.
"I thought he was just lacking a bit of pre-season practice. We were hoping to keep him on for 90 minutes, but he just fell a little bit short of that, but that's no great concern and we'll have another look at him tomorrow night."
Davies admitted he had been disappointed to see his side concede the goal from Vauxhall just before the break from a spotkick.
He added: "I'm not making any excuses because it's a matter of being professional, but a couple of the younger lads seem to suffer when the game is going so well and going so easy.
"The next few games will help us because we can't afford to switch off for one moment and they know that.
"I thought we switched off a couple of times at Vauxhall and got away with it the first time, but not the second time.
"I've had a word with the lads about the penalty decision which isn't a major concern, but if they are going to join the seasoned professionals it's things like that that they need to take on board.
"Whether it's a five a side game, in training, or a game at whatever level, they have to be concentrating for 90 minutes."
Meanwhile, Chris Holroyd and Paul Rutherford were due to travel down to AFC Bournemouth today and train with the South Coast club tomorrow as part of a one week trial.
Davies said: "Bournemouth have a small squad at the moment because of their troubles off the pitch. They only have 12 pros signed and are looking to get youth players involved, so there is obviously space for players at the right price and I think Chris and Paul would fall into that column.
"If they impress enough something may happen there.
"Sometimes it is a little concern that players join another League Two club because sometimes former players come back and score against their old club. But if it suits us and suits the players it may happen."
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