Forest are 13th in the table, six points adrift of the top six.
Davies, who twice guided the east midlands club to the play-offs during his first spell in charge at the City Ground, is confident of bridging that gap in the Reds' remaining 15 league fixtures.
"I am very confident, having spoken to the board," said the Scot, who feels Forest's players have been underachieving. "I've got no doubt in my mind that these people will do all they can to get the club to the Premier League.
"That's why I'm here, I wouldn't be here if I didn't think it was possible.
"But there's work to do, there's no doubt about that. You don't normally come into a club if there isn't work to do.
"There's an abundance of talent here, but these players have been underachieving. They have only been performing to 80-85 per cent of their capabilities in my opinion.
"It is my job, and the job of my coaching staff, to find that missing 15-20 per cent.
"Fawaz (Al-Hasawi, Forest's chairman) has already told me there is some money available should I feel we need to add to certain areas, but if we can get to where we want to go with the players that are already at the football club then we will do that."
Davies, back as Forest boss almost 20 months after he was sacked by the old regime, replaced fellow Scot Alex McLeish as manager on Thursday and officially began work on Monday.