Brendan Rodgers’ men were drawn in Group B and face glamour ties with European heavyweights Bayern Munich, big-spending French cracks Paris Saint-Germain and Belgian champions Anderlecht.
Davies knows the financial power of PSG – who smashed the transfer record to land Brazilian superstar Neymar from Barcelona for £198m – and Bayern dwarfs Celtic but believes they can upset the odds and be Champions League shocktroops.
Davies said: “It is an exciting challenge, not one which scares us. You are playing against teams which are favourites to beat you. You are the underdog against the likes of PSG and Bayern. It’s not something that is new to Celtic, going into these kind of games against really good teams.
“We are going to embrace it and look forward to it. It’s an exciting challenge for us all.”
Davies added: “Qualifying is a fantastic achievement and you have to look at what you are up against now.
“There is a massive gap which has opened up in Europe, more than ever, between some of these elite teams and the rest.
“You have to be mindful of that. The money they are spending on one player alone is incredible.
“But it’s not as if we have players who haven’t played at this level before. We’ve got some excellent players ourselves with Champions League and international experience.
“Neymar has gone to PSG with that enormous transfer fee but he is someone our players have played against, so that’s a good reference for them in terms of their level. That will give them confidence.
“You look at the draw and there are world-class players in every group.
“Brendan is a realistic, pragmatic manager. But at the same time he gives players belief and confidence. He has a lot of confidence in the way we play and what we can produce.”
Davies insists Celtic will aim higher than a shootout with Anderlecht for third place, and will tell the players to believe they can go through.
He said: “That’s what people will immediately look to [a fight between Celtic and Anderlecht for third].
“From our perspective it certainly won’t be the message that we’re giving to the players.
“That’s just not the way that we work, that we’re resigning ourselves to third place.
“The challenges are clear. We will be playing probably two of the biggest and best clubs in world football in our group.
“But, having said that, the record that we have got at Celtic Park is always something that works in our favour.”