Kenny Miller's 19th-minute opener got the rock-bottom Rams off to a bright start before Nicolas Anelka grabbed a fortunate equaliser 13 minutes later with his deflected effort.
Most pundits have already written off Davies' side but the Rams boss remains bullish about their chances, insisting: "We'll take the bumps and bruises along the way and have a right go.
"Many questioned the spirit of our team after letting in five at Arsenal last week but we showed today that we've got tremendous spirit at this club and we're working very hard.
"We created chances today and probably deserved to win the game, but every point matters at this level and we've got to be delighted with the response from the players and the way they went about their business."
Davies reserved particular praise for goalscorer Miller, who drilled home a fierce drive from Steve Howard's precise cross to get the home side off to such a fine start.
Davies added: "Kenny works his backside off to get his chances and his attitude is immense. We just need a bit more from one or two in different areas and we're still getting some guys fitter.
"It was very tense as we all know. It was a hard-fought encounter against a good side with lots of experience. So in the end it was a decent hard-earned point for us."
Bolton boss Sammy Lee cut a somewhat relieved figure and admitted that given the circumstances of the fixture he was quite happy to accept a point and an extension of his side's recent unbeaten run.
Lee said: "Prior to the game we would have accepted a point given the position we're in. We knew we were coming to a well-organised Derby team who are fighting for their lives just like us.
"I am very pleased with the chances we created and I have said on many occasions that our football and the amount of chances we have created really belies the position we are in.
"But I think we're getting better. Football is a game of confidence and that is vital for us to take into the next game. You gain confidence from points and we've got a very valuable point today which will hopefully be a great boost."