Wanderers are next-bottom of the Premier League but are by no means doomed to go down, and Davies has pledged to personally kick-start their scrap for survival.
"We are in a difficult position and that is a big challenge to myself and the team," said the striker.
"I'm the captain and I'm one of the ones who has to get the boys going, roll the sleeves up and get on with the battle.
"It is about getting Bolton out of the bottom three."
Davies said Coyle's return to the club, having previously been a player, has had a noticeable impact on the squad who have all risen to the challenge of trying to impress the new manager.
"From what I have seen in training everyone has been working hard to get themselves in his plans," added the 32-year-old, who was ill last week but had Coyle on the phone to him regularly.
"There are certain players under the previous manager (Gary Megson) who were frozen out and you could see their confidence draining away.
"Now I have seen a big change in some of the players: from the lads who have been starting to those on the fringes and those training with the reserves.
"I have been really impressed with the way the players have responded to him and I think that is a credit to him.
"Speaking to players individually they have been impressed with his man-management skills."
Coyle has had little time to work with his new players, having taken over just 10 days ago.
He knows it will take time to condition the squad to his style of football and drop the more direct approach of his predecessor.
Davies said they had not worked much on tactics, with Coyle focusing on giving his players more freedom.
"We have not overly worked on the shape because the manager recognises our strengths and does not want to take that away from the side," said the Bolton captain.
"He'll look to incorporate the way he wants to play over the coming games and I imagine we'll be working on things on the training ground.
"But he has said he wants us to go out there and express ourselves the way we can."
Coyle believes if the performance against Arsenal was an indicator of things to come then Bolton should soon start to see a more positive return.
"If we were to carry on at that level, game in, game out, in the Premier League that would result in a lot of points," said the Wanderers boss.
"We can take a lot of confidence from that performance.
"You don't come in, click your fingers and everything falls into place. There will be a gradual evolution at the club.
"But in the short term we have to pick points up and take ourselves up the league."