While the Scottish champions have a free week to prepare for the first meeting of the season between the Glasgow rivals, the Hoops face a tough midweek clash with Atletico Madrid.
Like Rangers, Celtic initially failed to make the group stages of the Europa League but were reinstated following the expulsion of opponents Sion.
They are now preparing to travel to Spain for a difficult opening match on Thursday - subject to Sion's appeal hearing two days earlier - before making the trip to Ibrox.
But Gers midfielder Davis said: "When teams are involved in Europe after Christmas, maybe it starts to take its toll then, not so much at the start of the season.
"I'm sure from Celtic's point of view they are delighted to be in the competition and they will be looking to get a good result out there to take into the Old Firm game.
"We would much rather be involved in Europe ourselves."
Rangers head into the game boosted by a 1-0 win over Dundee United on Saturday, which keeps them top of the Clydesdale Bank Premier League ahead of the highly-anticipated clash.
Davis added: "We just want to carry on the confidence.
"We've had a few new additions over the transfer window and everyone is together now so we can start working as a group and look forward to the first Old Firm match.
"There is still a lot more to come from this group of players but now we've got the squad together and the window is closed, the manager can do the work that he wants to do with us on the training field.
"There is no doubt we can play better overall but we have managed to keep on picking up wins and that's the most important thing."
Kyle Lafferty grabbed the only goal of the game with an hour gone after United's Johnny Russell was shown a straight red card in the first half.
Davis said: "It was always going to be another hard game for us and, even when Dundee United went down to 10 men, they made it difficult for us in terms of breaking them down. We are delighted to come away with the win."
Davis should have joined fellow Northern Irishman Lafferty on the scoresheet but was denied by a great save from the goalkeeper before watching in disbelief as his shot hit both posts before failing to cross the line.
He said: "I probably should have scored but the most important thing was to come away with the win.
"Hopefully I can get a few more goals this season.
"I had a couple of chances in this game and should have come away with one but the most important thing was to get the three points, especially going into the Old Firm game."
Despite ending the match empty-handed, United boss Peter Houston believes his side can take positives from the clash at Tannadice.
He said: "We dominated the first half and we were bossing the game.
"Even after Johnny was sent off, we had a few corners and goal-mouth chances.
"There were lots of positives and I'm just disappointed that we didn't take anything from the match."