Davies was put in charge of the Dragons in March when boss Dean Keates departed for League One side Walsall.
The club’s promotion push suffered as a result and they missed out on the play-offs by three points following Saturday’s goalless draw with AFC Fylde.
Davies is unsure on his own future at the Racecourse Ground but he hopes that whoever is appointed as the Dragons’ boss will have them competing for promotion next term.
He told BBC Wales: “When you look back at the season, we broke records for clean sheets and an unbeaten run but we didn’t have that killer instinct in front of goal. That has cost us and we know that.
“Ultimately, we haven’t won enough games. Have strides forward been made? Certainly. But have we failed with our objectives this season? We have.
“We’ve let ourselves down as a group of players and staff. The club will look to appoint a new manager as soon as possible.
“For players out of contract, that is important and then planning will be made for next season. For me personally, we’ll just wait and see.
“There are the foundations there for next season now for us to achieve what we want. There’s no reason why this club, with the supporter base that we’ve got, can't achieve promotion.”
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